since the value of this limit is infinite, then it must be of 0/0 form, in order to apply L'Hospital Rule... that means Nr=0 acosx+bxsinx-5 = 0 ..............(1)
Now differentiating the expression once and equating it with 0 again,we have,
-asinx+bxcosx+bsinx=0
differentiating once again,
-acosx-bxsinx+2bcosx=0 ................(2)
Solving 1 and 2,
2bcosx=5,
which is possible only when cosx=1,
hence b=5/2 and a=5 (be using the values in eqn (1))
Hopefully u'll get it now..... any problem do ask again.......