as a practical matter you may want to find t such that:
|sin(t)/t - 1| < 0.01
then use x = t/5.
finding such a t (and thus x) isn't that hard (i did it by trial-and-error in about 2 minutes), the real trick is showing the inequality holds in the interval (-x,x). unless i am mistaken, the problem doesn't ask you to find the largest possible such x, just one that works.