Answer
$x \approx 0.9$
See the picture below
Work Step by Step
Divide 5 on both sides of the equation:
$\dfrac{5e^{3x}}{5}=\dfrac{75}{5}$
$e^{3x}=15$
Here, we have to graph functions on the two sides of the equation.
So by graphing the functions $f(x)=e^{3x}$ and $g(x)=15$ (refer to the attached image), we can see that, there is one intersection point, therefore there will be one solution.
This is: $x\approx0.9$