Step 1: Determine complex ion charge from counter ion.
$SO_4^{2-}$ is outside the coordination sphere with charge $-2$. To form a neutral compound, the complex cation must carry charge $+2$.
Step 2: Assign ligand charges.
Five $NH_3$ ligands are neutral (charge = 0 each). One $ONO^-$ (nitrito) has charge $-1$. Total ligand charge = $-1$.
Step 3: Calculate oxidation state of Co.
$x + (-1) = +2$, so $x = +3$.
\[ \boxed{+3} \]