@bananajoy_2 You can have as many saves as you want. The game itself keeps the last five versions of each save before the most recent one, as backups. For example, your first save will be labeled Slot_00000002.save, and as you save your progress, the game will keep previous versions as Slot_00000002.save.verx, with x being a number from 0 to 4.
If you're looking for a particular save and don't find it in the Load Game screen, try temporarily removing some of your newer saves from the user data folder. (They're stored in Documents\Electronic Arts\The Sims 4\saves.) You can always put them back later. If the game is having trouble displaying all your saves, this may help. You can sort the saves folder by date, or remove one or two sets of saves, the main one and the .verx backups, at a time, until you find what you're looking for.