[tex]f(x)=\dfrac{5}{2}x+5\to y=\dfrac{5}{2}x+5\\\\\text{we exchange x with y and y with x}\\\\\dfrac{5}{2}y+5=x\\\\\text{solve for y}\\\\\dfrac{5}{2}y+5=x\ \ \ \ |-5\\\\\dfrac{5}{2}y=x-5\ \ \ \ |\cdot2\\\\5y=2x-10\ \ \ \ |:5\\\\\boxed{y=\dfrac{2}{5}x-2}[/tex]
[tex]\boxed{f^{-1}(x)=\dfrac{2}{5}x-2}[/tex]
