I think that you are missing part of the problem. Are the values for x restricted???
Notice that f(1)=f(4), which means that for the y value of 5, there are two x's (1 and 4) that get mapped to it. As written, this function is not 1-1, does not pass the horizontal line test, and therefore is not invertible.
However, if you restrict your domain, you can solve for an inverse. For x>=(5/2), then
f(x)=(2x-5)+2=2x-3 and you can solve for the inverse.
If you have the restriction x<=(5/2), then f(x)=-(2x-5)+2=7-2x, and you can solve for the inverse.