Define the $\ell_{p}$ ball in two dimensions as the set of points $(x, y)$ such that $|x|^{p}+|y|^{p} \leq 1$. Which of the following is $\text{FALSE:}$
- The $\ell_{2}$ ball is contained in the $\ell_{3}$ ball
- The $\ell_{2}$ ball is contained in the $\ell_{1}$ ball
- The $\ell_{3}$ ball is contained in the $\ell_{4}$ ball
- The $\ell_{2}$ ball is contained in the $\ell_{5}$ ball
- The $\ell_{1}$ ball is contained in the $\ell_{3}$ ball