@Ashvins you make a lot of assertions - "At lower levels this is Bad, as in Really Really BAD"; "But Sharpshooter at lv4 is unwise"; "the consistent damage from a better chance to hit usually serves you better"; "Simply put ASI should always be your FIRST feat for almost any class"' "If I only get a 5 to 1 improvement in hits it serves me better in the long run on damage"'; "The best burst damage build will almost always loose out over a consistent damage build with a -25% fudge factor built in like Sharpshooter gives you"' "Without the gear and levels a -25% hit chance at low levels is just bad even with the added damage".
However you don't provide any support for these claims. So let's do, as you say, some "simple number crunching" and answer the question you pose - "What good is that +10 to damage when your hit chance takes a -5"? Let's find out if just hitting more means the ASI will in fact do more for you.
First, some assumptions - you're using Dual Hand Crossbows, you're dealing 1d6+1d4+5 damage. Since you, like all good explorers, carry around a candle you drop, turn on, and then dip your crossbows in before starting combat. You also bought the Gloves of Archery, thus the additional +2 damage, for a total of 7-15 damage, average 11, before Sharpshooter or the ASI. This is in my opinion pretty realistic for around level 4. If you haven't dipped your weapon or gotten the Gloves of Archery, obviously that favors Sharpshooter more, as it represents a higher percentage of your damage.
First, neutral, no high or low ground, no advantage or disadvantage. Spoilers just because it's a block of text.
If you need a:
2 to hit (95%) (before ASI or sharpshooter)
With ASI - Still a 2 to hit, 1 always misses. You hit 95% of the time for an average of 12 damage, or 11.4 average damage.
With Sharpshooter - Now a 7 to hit, or 70%. The average damage is 21, so 14.7 average damage
5 to hit (80%)
With ASI - Now a 4 to hit (85%), average damage 12 on a hit, total average damage 10.2
With Sharpshooter - Now a 10 to hit (60%), average damage 21 on a hit, total average damage 12.6
10 to hit (60%)
With ASI - Now a 9 to hit (65%), average damage 12 on a hit, total average damage 7.8
With Sharpshooter - Now a 15 to hit (30%), average damage 21 on a hit, total average damage 7
15 to hit (30%)
With ASI - Now a 14 to hit (35%), average damage 12 on a hit, total average damage 4.2
With Sharpshooter - Obviously you toggle it off at this point, so 30% chance to hit, average damage 11 on a hit, total average damage 3.3
19 to hit (10%)
With ASI - Now an 18 to hit (15%), average damage 12 on a hit, total average damage 1.8
With Sharpshooter - Still off of course, average damage 11 on a hit, 10% chance to hit, total average damage 1.1
Now, the above is assuming standard shots, obviously low ground shooting up is better for Sharpshooter, and since better to hit numbers favor sharpshooter, so is high ground shooting down (you just move up the chart a bit more). However, it also assumes you aren't leveraging the most valuable thing you can obtain - Advantage. Let's say, for example, you have a party member webbing enemies, or blinding them, or attacking from hidden, or guiding bolt, or using certain pieces of equipment like the Risky Ring, and so on and so forth. Let's rerun the numbers again and see how they fair. Spoilers again just because it's a block of text.
2 to hit (99.75%) (before ASI or sharpshooter)
With ASI - Still a 2 to hit, 1 always misses. You hit 99.75% of the time for an average of 12 damage, or 11.97 average damage.
With Sharpshooter - Now a 7 to hit, or 91%. The average damage is 21, so 19.11 average damage
5 to hit (96%)
With ASI - Now a 4 to hit (97.75%), average damage 12 on a hit, total average damage 11.73
With Sharpshooter - Now a 10 to hit (79.75%), average damage 21 on a hit, total average damage 16.74
10 to hit (79.75%)
With ASI - Now a 9 to hit (84%), average damage 12 on a hit, total average damage 10.08
With Sharpshooter - Now a 15 to hit (51%), average damage 21 on a hit, total average damage 10.71
15 to hit (51%)
With ASI - Now a 14 to hit (57.75%), average damage 12 on a hit, total average damage 6.93
With Sharpshooter - Obviously you toggle it off at this point, so 51% chance to hit, average damage 11 on a hit, total average damage 5.61
19 to hit (19%)
With ASI - Now an 18 to hit (27.75%), average damage 12 on a hit, total average damage 3.33
With Sharpshooter - Still off of course, average damage 11 on a hit, 19% chance to hit, total average damage 2.09
Now, that's the numbers, but let's review some other reasons why Sharpshooter is far, far better than those numbers even might indicate:
1) It's often less about "amount of damage dealt" and more about "average actions to kill a target". If I am attacking an enemy with 18 HP (not uncommon at that stage of the game), I need to hit them TWICE with the ASI vs ONCE with Sharpshooter. Now, if say with Sharpshooter my hit chance dropped from 75% chance to 50% chance, that means I'll need to shoot at them 2x on average, but without it 2x is the *best case*, and typically I'll need more. From an action economy standpoint, Sharpshooter represents more whole targets dead, more consistently.
2) Overkill is absolutely a thing, but because Sharpshooter is toggleable, if you don't need the bonus (they only have 7 hitpoints say) or the enemy only has a few HP left, you just toggle it off, and don't suffer the miss chance. As such it has the tools built in to adapt to the situation as needed.
3) Sharpshooter is better when you're doing better things (like getting advantage, highground, shooting at hittable targets), while the ASI is better when you're doing worse things (like shooting with disadvantage, or against very hard to hit targets). As such it rewards good play, instead of rewarding performing maneuvers that don't offer much return in the first place. Cool, the ASI represents .7 more average damage when shooting at something needing a 19 to hit, for a whopping average return on your action of 1.8 damage. But if that's all you're getting, is that the best use of your action anyway?
How realistic are any of those numbers, anyways? Remember, we need a 10 to hit (before ASI or sharpshooter) before the ASI closes the gap, 15 to hit before it offers a significant advantage. Well, by level 5, your proficiency should be +3. your Dex is at least +3, you're a Ranger so you have +2, you should have +1 weapons, and you control your own positioning so there's little to no reason not to have high ground for +2. However given that it's conditional (as is low ground, *any* elevation difference is a 2 point difference for Sharpshooter) let's call it +1. That's +10 to hit overall, meaning you need an AC of 20 before they *even out*, and an AC of 25 before the ASI is pulling ahead. There are only 2 bosses in all of Act 1 *or Act Two* that hit the
lower of those two targets, and one of them, let's just say that hitting him with arrows isn't exactly the best way to approach the fight. 22 bosses, however, are substantially below that target, meaning Sharpshooter is better against them. If someone casts Bless on you? The ASI is worse on every single boss, to say nothing of the common enemies throughout Act 1 and 2, where it's always better, often by large margins (expected damage +50% kind of margins).
Now, there's certainly merit to the idea that the ASI helps in tons of other ways - better AC, Dex Saves, Stealth and Sleight of Hand, better Dex is great! However, from a *damage output* standpoint, which is what this build ostensibly seeks to maximize, it is absolutely not superior. I took Sharpshooter with my Gnome Thief at 4, and the next dozen play sessions were filled with "OMG" "WTF" "Svirf makes me feel very inadequate" "That's disgusting" and so forth, as I took out 2+ targets pretty much every turn, and it hasn't really changed much since. They would be up against a tough foe, technically a boss, and would say "wait I think I have a plan" only to follow it up with "nevermind, or I just wait for Svirf to go and he kills it in one turn". Seriously, it's that gross, 70 damage in a turn if they all hit (and it's not that uncommon if you're setting up combat right) will win you a lot of fights in the early game, and very quickly at that. Just wanted to provide some counterperspective, outside the number crunching, from lived experience. I hope any of that wall of text helps.