First, you have to find the least common denominator of both three and five. In this situation, it would be fifteen because fifteen is a multiple of both three and five, and it is the least (not 'necessary', but it helps to keep numbers small). Secondly, you multiply the numerators of both numbers by the correct multiple it takes to get fifteen (for 2/3, it would be 5; for 1/5, it would be 3). The problem is then 10/15 + 3/15. The answer is 13/15.
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2 1/3 / 1 3/5 7/3 / 8/5 7/3 * 5/8 7*5 = 35 3*8 = 24 35 / 24 1 and 11/24 1 and 11/24 1 and 11/24
You must convert this mixed fraction to an improper fraction. Then, to get the reciprocal, just exchange top and bottom.