$$13=5+20m-2m$$
Combine $20m$ and $-2m$ to get $18m$.$$13=5+18m$$
Swap sides so that all variable terms are on the left hand side.$$5+18m=13$$
Subtract $5$ from both sides.$$18m=13-5$$
Subtract $5$ from $13$ to get $8$.$$18m=8$$
Divide both sides by $18$.$$m=\frac{8}{18}$$
Reduce the fraction $\frac{8}{18}$ to lowest terms by extracting and canceling out $2$.$$m=\frac{4}{9}$$