Chapter P, Prerequisites - Section P.3 - Integer Exponents and Scientific Notation - P.3 Exercises - Page 23: 2

Yes there is difference between $(-5)^{4}$ and$-5^{4}$.

Here, $(-5)^{4}$ = $(-5)\times(-5)\times(-5)\times(-5)$ = 625 $-5^{4}$ = -($5\times5\times5\times5$) = -625 and 625 $\ne$ -625, so there is difference between $(-5)^{4}$ and$-5^{4}$.