Algebra

Remember the Binomial Expansion Theorem and it's relationship to Pascal's Triangle. The $n$ th column will have a total sum of $2^{n-1}$ . Of course, the first column adds simply to $1$ . For the expansion, the sum will thus be $2^5$ which is $\boxed{32}$ . :D

$\large\displaystyle \sum _{n=0}^{5} \dbinom{5}{n}=\dbinom{5}{0}+\dbinom{5}{1}+\dbinom{5}{2}+\dbinom{5}{3}+\dbinom{5}{4}+\dbinom{5}{5}=2(1+5+10)=32$