Perpendicular lines have slopes that are opposite signs and reciprocals.
For example, the perpendicular slope to 2/3 is -3/2 (opposite sign and flipped upside-down).
The first step on your question is to find the slope of your line. You can do this by putting the equation into slope-intercept form:
![\begin{aligned}4x-5y &= 10\\[0.5em]-5y &= -4x+10\\[0.5em]y &= (4)/(5)x-2\endaligned}](https://img.qammunity.org/2022/formulas/mathematics/high-school/wkqrmhjnvhiis8m7zy9yp8spkg6pzgmjcg.png)
From this, we can see your slope is 4/5.
The perpendicular slope will be -5/4.