Question 78·Hard·Nonlinear Equations in One Variable; Systems in Two Variables

In the system of equations above, $b$ is a constant. The graphs intersect at two points $(x_1, y_1)$ and $(x_2, y_2)$, where $x_1 < x_2$ and both $x$-coordinates are positive. If $x_2 - x_1 = 5$, what is the value of $b$?