Using Pascal's triangle, what is the coefficient of $x^2a^3$ in the expansion of $(x+a)^5$? 

In $(x+a)^5$, the coefficients are given by the 5th row of Pascal's triangle: $1, 5, 10, 10, 5, 1$. The term $x^2a^3$ corresponds to choosing 3 factors of $a$ (or 2 factors of $x$), so its coefficient is $\binom{5}{3}=10$.