You might have e.g. 5 spells that you know and have memorized, but only 3 spell slots, so you can really only cast 3 of those.
Additionally after you use them up, you can't just use them in the next fight, but have to go rest, which can't happen every 5 minutes, so basically you don't have as many spells as you might think.
At first it's even a bit too few, but later it gets great, and you'll appreciate it too one day.