Singular Values & the SVD · Superchallenge problem

Let $T$ be the $5\times 5$ matrix with $t_{ij} = 1$ when $|i - j| \le 1$ and $t_{ij} = 0$ otherwise (ones on the main diagonal and the two diagonals next to it). Find the nuclear norm $\|T\|_* = \sum\sigma_k$. Give your answer in simplest radical form.