Answer
$f'(1)=-1$
Work Step by Step
To find the slope of a function at any given point, all one has to do would be to look for the value of the derivative function at the same x value.
Given that $f(x)=5x-3x^2$, then the derivative function by the power rule will be $f'(x)=5x^{1-1}-3(2)x^{2-1}=5-6x$
As such, the slope at the point $x=1$ would be $f'(1)=5-6(1)=-1$
