How do you solve #e^x + lnx = 5#?
The root could not be got in mathematical exactitude. Only an approximation to any sd-accuracy could be obtained. Graphical methods lack accuracy. Iterative methods are fine.
Bisection method is explained here. This is quite easy for anyone. There are other faster numerical methods..
Use your discretion for a short enclosure.
Choose (1.5, 1.6) for sign test, and so on, until you get the desired accuracy.
I find f(1.5215)f(1.5220) < 0. So rounded 4-sd approximation of the root is 1.522..
This algorithms for the bisection method and its variations are programmable, for any befitting computer language...