How many solutions are there for the following

n! + 10 is perfect square of an integer

answer one solution (3 by try and error)

for any number greater than 5 (4! + 10 is not perfect square) last digit becomes 0. For this the number should be square of intergral multiple of 10. Then the power will determine number of 0's in the end. But any answer of form n!+10 (n4) has only on zero in the end. Root of 10 is itself irrational therefore even if we divide and multiply the number by 10 root 10 will make the number irrational.Hence no other possiblities are left.