Let \(\rm \vec{a}=\hat{i}+2 \hat{j}+3 \hat{k}, \vec{b}=3 \hat{i}+\hat{j}-\hat{k}\) and \(\overrightarrow{\mathrm{c}}\) be three vectors such that \(\overrightarrow{\mathrm{c}}\) is coplanar with \(\overrightarrow{\mathrm{a}}\) and \(\overrightarrow{\mathrm{b}}\).  If the vector \(\overrightarrow{\mathrm{c}}\) is perpendicular to \(\overrightarrow{\mathrm{b}}\) and \(\overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{c}}=5\), then \(|\overrightarrow{{c}}|\) is equal to