$$\cfrac { 5 }{ 3 } +\cfrac { 3 }{ 5 } =\cfrac { 5\times 5 }{ 3\times 5 }
+\cfrac { 3\times 3 }{ 5\times 3 } =\cfrac { 25 }{ 15 } +\cfrac { 9 }{
15 } =\cfrac { 25+9 }{ 15 } =\cfrac { 34 }{ 15 } =2\cfrac { 4 }{ 15 } $$
L.C.M of $$3$$ and $$5$$ is $$15$$.