Let the position vectors of three vertices of a triangle be \(4\mathbf{p} + \mathbf{q} - 3\mathbf{r}, -5\mathbf{p} + \mathbf{q} + 2\mathbf{r}\) and \(2\mathbf{p} - \mathbf{q} + 2\mathbf{r}\). If the position vectors of the orthocenter and the circumcenter of the triangle are \(\frac{5\mathbf{p} + 2\mathbf{q} + 3\mathbf{r}}{14}\) and \(\alpha\mathbf{p} + \beta\mathbf{q} + \gamma\mathbf{r}\) respectively, then \(\alpha + 2\beta + 5\gamma\) is equal to