Vector Spaces & Bases · Superchallenge problem

In $P_5$ (real polynomials of degree at most $5$) the six polynomials $c_k = (1+x)^{5-k}(1-x)^k$, $k = 0, 1, \ldots, 5$, form a basis $C$. Write $x^2 = \sum_{k=0}^5 t_k c_k$. Find $t_2$, the coefficient of $(1+x)^3(1-x)^2$.