Vector Algebra

Let $\overrightarrow \alpha = 4\widehat i + 3\widehat j + 5\widehat k$ and $\overrightarrow \beta = \widehat i + 2\widehat j - 4\widehat k$. Let ${\overrightarrow \beta _1}$ be parallel to $\overrightarrow \alpha$ and ${\overrightarrow \beta _2}$ be perpendicular to $\overrightarrow \alpha$. If $\overrightarrow \beta = {\overrightarrow \beta _1} + {\overrightarrow \beta _2}$, then the value of $5{\overrightarrow \beta _2}\,.\left( {\widehat i + \widehat j + \widehat k} \right)$ is :