For easy calculation let's take the total no. of painting = 120

Now Total painting sold = $\frac{5}{8} * 120 = 75$

Therefore number of paintings not sold = $120 - 75 = 45$

Total number of impressionist painting = $\frac{3}{5} * 120 = 72$

Number of impressionist paintings sold = $\frac{2}{3}* 72 = 48$

Therefore number of impressionist paintings not sold = $72 - 48 = 24$

Therefore, the fraction of paintings that were not sold were impressionist = $\frac{24}{45} = \frac{8}{15}$