The weights cancel against the white fraction

Let $U_1,U_2,\dots ,U_5$ be 5 urns such that urn U_k contains $2k+k^2$ balls, out of which 2k are white balls and $k^2$ are black balls, k = 1, 2, …, 5. An urn is selected with probability of selecting urn U_k being proportional to (k + 2). A ball is chosen randomly from the selected urn. Then, the probability that the urn $U_5$ was selected, given that the ball drawn is white, is equal to