how do you solve this problem 53!/(53-5)!5!

The top is 53!. The bottom is 48!5!. So the 48 cancels with the 53 on top except for 53×52×51×50×49. That should be more manageable. Then divide that big number by 5!, which is 120.

It's the combinatoric for C(53, 5)

Just use the "ncr" button on the bottom left of the onsite calculator keypad and then key in  "53, 5"  .....hit "enter" after that (or " = " )