The equation can be simplified by factoring out $5^x$, resulting in $5^x(5 + 1) = 150$ or $6 \cdot 5^x = 150$. Dividing both sides by 6 gives $5^x = 25$, which can be expressed as $5^2$. Therefore, $x$ must equal 2, since $5^x = 5^2$.