If 5a = 3125, then the value of 5(a - 3) is:

When two powers of the same base are equal, their exponents must be equal: if am = an (with a not equal to 0, 1, or -1), then m = n. The quotient rule am divided by an = a(m - n) then lets a power at a shifted exponent be evaluated directly from a power that is already known.

1. Express 3125 as a power of 5: 3125 = 55.

2. 5a = 3125 = 55, so by the equal-bases rule, a = 5.

3. Substitute a = 5 into the target expression: 5(a - 3) = 5(5 - 3) = 52.

4. Evaluate 52 = 25.

Cross-check with the quotient rule directly: 5(a - 3) = 5a divided by 53 = 3125 divided by 125 = 25, the same value.