To find the lengths of BC and AC, we will use the sine and cosine trigonometric ratios.

Given:
Angle C = 90°
Angle A = 60°
Side AB = 5√3

First, let's find the length of side BC $oppositeangleA$:

sin$60°$ = BC / AB
sin$60°$ = BC / 5√3
BC = 5√3 sin$60°$ BC ≈ 5 0.866
BC ≈ 4.33

Next, let's find the length of side AC $oppositerightangleC$:

cos$60°$ = AC / AB
cos$60°$ = AC / 5√3
AC = 5√3 cos$60°$ AC ≈ 5 0.5
AC ≈ 2.50

Therefore, the length of side BC is approximately 4.33 and the length of side AC is approximately 2.50.