x must be less than 5 (it is from choices: 0,1,2,3,4). Why?

x>=5 --> x! is a multiple of 10, and so is 6(x!). The equation:

6(x!)=y^2 -13 means that for x>=5, y^2 must end in 3, which is impossible for integers.

What works is (2,5) and (3,7) and also (2,-5) and (3,-7)

*Edited on ***October 21, 2018, 3:32 am**