look here, for a long-winded discussion of this issue:
To summarize for you though, your apps are stored in a hidden and limited space, that is independent of the two public spaces you can see, and where you have lots of room. And it is full, because kids books (or whatever apps) are enormously large.
The good news for you may be that if you take your NOOKcolor in to a B&N store, they will adjust it for you, so that 4 of the 5 GB in your visible space will vanish, and be moved to the internal private space, where all your apps (and B&N-purchased books) will then be stored.
There are a couple potential downsides that may concern some folks, but you'll need to do a bit of reading in the linked-topic to discover those, and see if they are important to you. Or perhaps someone else will chime in here.
I had the same problem - remembered somewhere someone mentioned taking out the sd card then downloading the app. That solved the problem. Put the sd card back in - no problems. Pudda