5^x-3=1/25 [tex]{5}^{x - 3} = \frac{1}{25} [/tex]

The first step for solving this is to write the expression on the right side of the equation in exponential form.
[tex]5^{x-3} = 5^{-2} [/tex]
Since the bases are the same,, set the exponents equal to each other.
x - 3 = -2 
Now move the constant to the right side and then change its sign.
x = -2 + 3
Now calculate the sum to get your final answer.
x = 1
This means that the correct answer to your equation is going to be x = 1.
Let me know if you have any further questions.
:)