Let C = number of cents on the check and D = number of dollars. The amount of money he should have received

__in cents__ is 100D + C, but he actually receved 100C + D. So after spending the nickel and realizing he has twice as much money as he should have the equation you need to solve is:

100C + D - 5 = 2(100D +C)

Rearrange: 98C = 199D + 5

Both C and D must be integers, and both must be in the range (0,99) inclusive. At this point you can use trial and error, but first note that the left side is even, which means 199D must be odd, so D is odd. Also, since 98 has prime factors 2 and 7, D cannot be a multiple of 7 (since 199D +5 would not be a multiple of 7). After that, I think it's just trial and error to find integer solutions for C and D, but to save you a little time I suggest you start with trying D = 25, then 27, etc. - you should get it shortly