jmc

Writing the right side with $5$ as the base, we have $125^x=(5^3{)}^x=5^{3x}$, so our equation is: $$5^{x+4}=5^{3x}.$$Then, setting the exponents equal, we obtain $$x+4=3x.$$This yields $2x=4⟹\boxed{x=2}$