Hello everyone, since every other type of marathon has been done on this site and there has been a lull in the activity around here, I propose a limit marathon. Same concept as all the other; after someone completes a limit and gets the OK from the limit's poster, he/she posts their own limit. The restrictions are, no L'hopital's unless stated otherwise (yes jump for joy) and no graphical help. Also, it would be nice if the poster of the limit would provide their solution. For the first one, we will start off with something simple

Find $\displaystyle \lim_{x\to{0}}\frac{\sin(2\sin(3\sin(4\sin(5x))))) }{x}$