Keep calm and Apply Chain Rule

The easiest way to do this is simply to solve for the derivative of $f$ , then evaluate it at $x=5$ . We note that the function can be written as a composition of functions, and thus is solvable using chain rule:

$\frac{d}{dx}f(x)=e^{(2\sin(x^{(3 \log 5)}))} * 2\cos(x^{(3 \log 5)}) * (3 \log 5) x^{(3 \log 5 - 1)}$

Evaluating at $x=5$ , being careful with entering the numbers in our calculator, we get an approximate answer of -6572.05.