Question 152520
Quickest way to check is to plug your solution into the equation and make sure it solves it. 
{{{e^(2x+5)}}}
{{{e^(2(-1.344)+5)}}}
{{{e^(-2.688+5)}}}
{{{e^(2.312)}}}
{{{10.094}}}
Oops, there's a problem. 
You paid attention for logarithms but not during subtraction. 
Your thinking and approach to the problem are clear. 
{{{ln(e^(2x+5))=ln(40)}}}
{{{2x+5=ln(40)}}}
{{{2x+5 = 3.688}}}
{{{2x = highlight(-2.688)}}}
It should be,
{{{2x = highlight(-1.311)}}}
{{{x = -0.656}}}
Checking, 
{{{e^(2x+5)}}}
{{{e^(2(-0.656)+5)}}}
{{{e^(3.688)}}}
{{{39.96}}}
Close enough.