a)

$\frac{1}{3}+2\frac{1}{5}=\frac{1\cdot 5}{3\cdot 5}+2\frac{1\cdot 3}{5\cdot 3}=\frac{5}{15}+2\frac{3}{15}=2\frac{8}{15}$

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b)

$7\frac{2}{3}-5\frac{5}{6}=7\frac{2\cdot 2}{3\cdot 2}-5\frac{5}{6}=7\frac{4}{6}-5\frac{5}{6}=6\frac{10}{6}-5\frac{5}{6}=1\frac{5}{6}$

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c)

$3\frac{1}{4}+2\frac{1}{9}=3\frac{1\cdot 9}{4\cdot 9}+2\frac{1\cdot 4}{9\cdot 4}=3\frac{9}{36}+2\frac{4}{36}=5\frac{13}{36}$

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d)

$5\frac{1}{7}-1\frac{2}{9}=5\frac{1}{7}-1\frac{2}{9}=5\frac{1\cdot 9}{7\cdot 9}-1\frac{2\cdot 7}{9\cdot 7}=5\frac{9}{63}-1\frac{14}{63}=4\frac{72}{63}-1\frac{14}{63}=3\frac{58}{63}$

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e)

$4\frac{3}{5}+2\frac{3}{4}=4\frac{3\cdot 4}{5\cdot 4}+2\frac{3\cdot 5}{4\cdot 5}=4\frac{12}{20}+2\frac{15}{20}=6\frac{27}{20}=7\frac{7}{20}$