Answer
$5\times\frac{5^{k}-25}{4} $
Work Step by Step
We know that, $1 + r + r^2 + ··· + r^n = \frac{r^{n+1}− 1}{r − 1}$
$5^3 + 5^4 + 5^5 + ··· + 5^k $ = $5^3(1+5^1 + 5^2 + ··· + 5^{k-3}) $
=$5^3\times\frac{5^{(k-3)+1}-1}{5-1} $
=$5^3\times\frac{5^{k-2}-1}{4} $ or $\frac{5^{k+1}-5^3}{4} $
=$5\times\frac{5^{k}-5^2}{4} $
