Just plain enumeration without any other optimizations, there's 44 cards left in the deck, so that's 44C5 combinations (choose 5 out of 44). That comes out to 1086008, if you got something higher then you are counting some identical boards multiple times.
This is one of the reasons it's nice there are so many good existing programs like PPT. I bashed my head against problems like these, and knowing what the right answer was helped me to develop test cases and work on my own code until they passed. Without those test cases I guess I would have been doing a lot of pen and paper calculations and maybe some advanced guessing.