Find the limit: as x approaches 0 lim((5/x)-(5/sin(x))

5/x - 5/sinx

= 5 * (sinx-x) / xsinx

now use l'Hospital's Rule

5(cosx-1)/(sinx + xcosx)

and again

-5sinx/(cosx+cosx-xsinx)
= 0/2
= 0