Lambert W Function

[thry123]

In my work I have faced an optimization problem to resolve which I have to solve the following expression
 
[math](x+5)^x=7[/math].

 I know that to get  I can use the Omega function Lambert W Function, however, I can't understand how it works. Thus, I ask for help of those of you who know how to solve this kind of equations (showing as much steps as you can) in order to give me reference point for further studying of this topic.