find the volume of the solid obtained by rotating the region bounded by xy=1,x=0,y=1,y=5 around x-axis?

Sketch it. This is the most important part and serves for the understanding of what follows.
Now, I choose to use the (hollow) cylinder procedure: a horizontal strip at height y, of width dy, somewhere from y=1 to 5. Its length is thus x = 1/y. Rotating this makes a hollow cylinder of radius y.

Thus the small volume of this hollow is 2πy * x * dy = 2πy * (1/y) * dy. Simply integrate this now from y=1 to 5.
Done!

Hopefully no one will spoil you the answer thereby depriving you from your personal enhancement; that would be very inconsiderate of them.