The answer is approximately 5.08914650686019
Round this value however you need to
----------------------------------------
Work Shown:
f(x) = tan(5x)
f ' (x) = 5*sec^2(5x)
f ' (5) = 5*sec^2(5*5)
f ' (5) = 5*sec^2(25)
f ' (5) = 5*(1/(cos^2(25)))
f ' (5) = 5/(cos^2(25))
f ' (5) = 5/((cos(25))^2)
f ' (5) = 5/((0.9912028118635)^2) ... see note below
f ' (5) = 5/0.9824830142461
f ' (5) = 5.08914650686019
Note: make sure your calculator is in radian mode