Formation of Lactone from 5-amino-decanoic acid?
I doubt your book is asking you to convert this molecule into a lactone. This would be very hard to do. It could, however, be easily converted into a lactam. 5 and 6 membered lactams are formed by simple dehydration. For your γ-lactam, this can be achieved by heating the amino carboxylic acid, forming the thermodynamically favourable, stable 6-membered lactam. Similarly, lactones can be be interconverted by adjusting the pH.



IF you really wanted to convert the amine into a lactone, it would involve some pretty uncommon reagents. This blog post mentions that pyrylium salts can be used to make a primary amine into a leaving group, which would, presumably, allow you to substitute a hydroxyl group, thereby giving you access to the lactone. 
http://curlyarrow.blogspot.hu/2009/09/how-to-turn-amine-into-leaving-group.html