You can solve this by cross multiplying the two fractions.
a / 5/8 = 3/5 / 2/3
2/3 *a = 3/5 * 5/8
2a/3 = 15/40
Multiply the 3 from the left side's denominator into the right side's numerator.
2a= 45/40
Divide both sides by 2
a= 45/80
Simplify
a = 9/16