Solving a logarithmic equation with variables on each side

Okay, so while doing a problem for my calculus class I was required to graph two functions in order to see where they intersect, as according to my teacher there is no way to solve it analytically.

This really bothers me and there must be a way to solve it. I did research online to try to solve it, but I had no idea where to even start.

Here is the equation.

$$y=\mathrm{ln}(5-y)$$

Okay, so while doing a problem for my calculus class I was required to graph two functions in order to see where they intersect, as according to my teacher there is no way to solve it analytically.

This really bothers me and there must be a way to solve it. I did research online to try to solve it, but I had no idea where to even start.

Here is the equation.

$$y=\mathrm{ln}(5-y)$$