find the slope that is perpendicular to the graph of the equation y-2x=-5

We can rearrange the initial equation to y=mx+b

y=2x-5

Since perpendicular slopes must equal -1,
x=the perpendicular slope
2x=-1
x=-1/2

(Or you can just take the negative reciprocal above is just the "formula form" for it)

Therefore, the perpendicular slope is -1/2