If the value of the integral \( \displaystyle \int_{0}^{5} \frac{x + \lfloor x \rfloor}{e^{\,x - \lfloor x \rfloor}} \, dx = \alpha e^{-1} + \beta \), where \( \alpha, \beta \in \mathbb{R} \), \( 5\alpha + 6\beta = 0 \), and \( \lfloor x \rfloor \) denotes the greatest integer less than or equal to \( x \); then the value of \( (\alpha + \beta)^{2} \) is equal to:
