$\hat \gamma_0=\begin{bmatrix}
I_2 & 0 \\
0 & -I_2
\end{bmatrix}, \quad \hat \gamma_k= \begin{bmatrix}
0 & -\sigma_k \\
\sigma_k & 0
\end{bmatrix}, \quad \hat \gamma_5 = \begin{bmatrix}
0 & I_2 \\
I_2 & 0
\end{bmatrix}$
Then we have $\hat \gamma_0 \hat \gamma_1 \hat \gamma_2 \hat \gamma_3 = \begin{bmatrix}0& iI_2 \\
iI_2 & 0\end{bmatrix} = i \gamma_5$