Let's look at these separately.
Initial space used: for one thing, it would be good to know how exactly the space was being counted, since different apps/menus can give different answers. The way the system menu presents this varies between devices, but if you used that then I would expect the "used" space to include the entire sizes of the various system partitions, not just the space in those partitions that's in use but any free space in them too. This does make sense, because you can't use that space for your own data or apps, it's basically reserved for any future updates, so as far as you are concerned it's "used" (but it can confuse people when the phone tells them this is all "system data", as some do). Another thing to watch is binary vs decimal units: that "64 GB" is going to be in decimal units, but computers actually use binary, and 64G decimal corresponds to 59.6G binary (decimal G = 10^9, binary = 2^30 which is 7% larger). So if it quotes space in binary and you don't know this it looks like 4.4GB has disappeared. You can tell which it's using if it shows you the total, but otherwise it may not be obvious.
As for the downloaded apps, how did you estimate the size of them? The Play Store will tell you the size of the package you download, but the installed size is always larger, and if the app then downloads any data that also uses space. 3 apps using 2GB, never mind 5GB, says that they are large, probably games, in which case a download of data files after installation isn't that unusual. If you look in Settings > Apps you should be able to see how much space each is using, for app and for their data, and if that adds to 5GB for the 3 of them then you have the answer.