I have to find this limit without using l'Hôpital's rule:
$\lim_{x\to0}\frac{\sqrt{5x+3}-\sqrt 3}{5^{\sin(7x)}-1}$
I have no idea how to do it. L'Hôpital's rule makes it easy, but how should I go about calculating this without using the rule?
I should add that I'm not supposed to use anything but the most basic methods and facts. I was thinking I should use the squeeze theorem, but I'm not seeing any estimates that work.