По теореме Виета:

[tex]{x}^{2} + bx + c = 0\\ x_{1} + x_{2} = - b\\ x_{1} x_{2} = c[/tex]

[tex] {x}^{2} - 5x - 2 = 0 \\ x_{1} + x_{2} =5 \\ x_{1} x_{2} = - 2 \\ \\ \frac{1}{x_{1}} + \frac{1}{x_{2}} = \frac{x_{2} + x_{1}}{x_{1}x_{2}} = \frac{5}{ - 2 } = - 2.5[/tex]