$$8x-3=5-2x$$
Add $2x$ to both sides.$$8x-3+2x=5$$
Combine $8x$ and $2x$ to get $10x$.$$10x-3=5$$
Add $3$ to both sides.$$10x=5+3$$
Add $5$ and $3$ to get $8$.$$10x=8$$
Divide both sides by $10$.$$x=\frac{8}{10}$$
Reduce the fraction $\frac{8}{10}$ to lowest terms by extracting and canceling out $2$.$$x=\frac{4}{5}$$