First, let's multiply your asymptote by x/x (which doesn't change it):

x^2/(2x) -5x/x

Get a common denominator and combine terms:

x^2/(2x) - 10x/(2x)

(x^2-10x)/(2x)

Now, we can use constants on the top, which won't change the asymptote:

(x^2 - 10x + 5) / (2x)

That has the oblique asymptote 1/2 x - 5

There are infinitely many functions with that asymptote.

Read more: how to find the rational function of y 1/2x-5 as a oblique - JustAnswer https://www.justanswer.com/math/2rkgb-find-rational-function-y-1-2x-5-oblique.html#ixzz1exd1fELo