x+y = 17 - that expresses the number of bills.
1x + 5y = 53.
Solve the first for x in terms of y and substitute that into the second.
x = 17 - y
17 - y + 5y =53
17 +4y = 53
4y = 36
y = 9
Substitute that back into the first equation: x + 9 = 17 and then x = 8