What is 25 to the power of x equals a fifth

Since  25 is a power of 5, the key here is to see if we can equate bases.....

25^x  = 1/5             note that 25  = 5²    and  1/5  =  5^-1  .....so we can write

(5²)^x   =  5^-1

5^2x  = 5 ^-1         since the bases are the same, we can equate exponents

2x  = -1              divide both sides by 2

x  =  -1/2