To raise a power to another power, multiply the exponents. Multiply $2$ and $2$ to get $4$.
$$\frac{\mathrm{d}}{\mathrm{d}x}(x+5^{4})$$
Calculate $5$ to the power of $4$ and get $625$.
$$\frac{\mathrm{d}}{\mathrm{d}x}(x+625)$$
The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is $0$. The derivative of $ax^{n}$ is $nax^{n-1}$.
