Master's institution forcing me to deposit $5000 immediately -- what can I do if I accept?
I do not think the quick monetary outlay is common. You seem to be leaning toward acceptance and then backing out if you get a better offer. This may be possible because, in my experience, there is not a centralized system which lets other schools know you have accepted (although perhaps that could be different for Masters programs where you are using federal aid, not sure). 

However, I would encourage you to take an alternative approach. Call them and explain that you are waiting to hear from other programs, some of which would be funded. Ask for a deadline extension until the April 15th deadline. In the past I was successful with this strategy, and I know students in our program have also successfully received extensions.