a+b+c = 73 (a is shortest side, b is second shortest side, c is longest side)
c = a+b-5
c = 2a+8
b = a+13
2a+8+a+13+a = 73
4a+21=73
4a = 52
a = 13
b = 26
c = 34
However when you plug that back in, you don't get a triangle, so I think you are missing something