What is the derivative of 5x ?

Explanation:
Given: ${\displaystyle \frac{d}{dx}\left(5^x\right)}$
Apply the general formula that ${\displaystyle \frac{d}{dx}\left(a^x\right)=a^x\ln a\text{ for }\in \mathbb{R}}$
${\displaystyle \therefore \frac{d}{dx}\left(5^x\right)=5^x\ln 5}$

Explanation:
Let ${\displaystyle y=5^x}$
differentiate implicity with respect to x
take ${\displaystyle \ln }$ (natural log) of both sides
${\displaystyle \ln y={\ln 5}^x=x\ln 5}$
${\displaystyle \Rightarrow \frac{1}{y}\frac{dy}{dx}=\ln 5}$
${\displaystyle \Rightarrow \frac{dy}{dx}=y\ln 5=5^x\ln 5}$

For a generalized answer to this question, you can use the following which works in cases of $5^x$ and $x^5$:
$\frac{d}{dx}(f(x{)}^{g(x)})=f(x{)}^{g(x)-1}(g(x)f^{\prime }(x)+f(x)\log (f(x))g^{\prime }(x)$
So
$\frac{d}{dx}{x}^5=x^{5-1}(5\times 1+x\log (x)\times 0)$
$=x^4(5+0)$
$=5x^4$
And, likewise:
$\frac{d}{dx}{5}^x=5^{x-1}(x\times 0+5\log (5)\times )$
$=5^{x-1}(0+5\log (5))$
$=5^x\log (5)$
Note $5\times 5^{x-1}\equiv 5^x$