What is the value of b if $5^b + 5^b + 5^b + 5^b + 5^b = 625^{(b-1)}*25^{b}$ ? Express your answer as a common fraction.
5b + 5b + 5b + 5b + 5b = 625b - 1 * 25b
5 * 5b = (54)b - 1 * (52)b
5b + 1 = 54b - 4 * 52b
5b + 1 = 54b - 4 + 2b
5b + 1 = 56b - 4
b + 1 = 6b - 4
5 = 5b ---> b = 1