First of all: "Level" isn't something that monsters/enemies in DnD used. DnD 5e uses Challenge Rating, which isn't the same. A CR4 is considered a medium challenge for a medium sized party of level 4. "Level" in BG3 is something similar, but not the same.
A Young Red Dragon is CR10. My experience is depending on party and players you can take on single targets of quite higher CR than their average level. I pitted my current group up against a Young Black Dragon (CR7) when they were 5 level 3 characters. Sure I nearly killed one player, but they didn't have too hard of a time.
So I think it's doable.
Now the Red Dragon we see the Gith riding looks bigger than a "large" creature, which is what Young Dragons are. A horse is Large, so is an Ogre. So you could ride a Young Dragon for sure.
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Sometimes you want to have a monster at just the right time, and be a decent challenge. As a DM that's when you homebrew things. If you need bigger draggons, just make the Young Dragon Gargantuan, problem solved. People really shouldn't be married to the Monster Manual, not as table top gamers, or as video gamers. The MM is great for DMs, because we can quickly make an encounter, but when we want that little something extra we make our own.
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For reference a Mind Flayer is CR 7, having one being "level 5" isn't too far from reality. Again: Home Brew works best when you need to tell a story.
