Key hint missing. Wording in solution should be improved.
Fragment of a discussion from Science talk:Math Exam Resources/Courses/MATH101/April 2012/Question 1 (i)
Thanks, please feel free go ahead to make the changes you envisioned. I agree enough to let you take over. I don't have time to implement it myself now.
The L'Hospital rule does invoke chain rule and possibly "impossibly-many" complications, however, a simple call to an algebra system gives the denominator to be something like (smaller terms) + 120*x*cos(x^5). So it either requires an inhuman length of calculation or an understanding to ignore "higher order terms" which is not probably not available to most students. (The numerator is simple though, and 4 differentiations suffice to end the case).
So I agree we should simply omit it and say it's "impossible", in some sense.