$$(14\frac{2}{3}-5\frac{5}{9})-(3\frac{7}{8}+1\frac{1}{2})=(14\frac{6}{9}-5\frac{5}{9})-(3\frac{7}{8}+1\frac{4}{8})=9\frac{1}{9}-4\frac{11}{8}=9\frac{1}{9}-5\frac{3}{8}=9\frac{8}{72}-5\frac{27}{72}=8\frac{80}{72}-5\frac{27}{72}=3\frac{53}{72}$$
Ответ: $$3\frac{53}{72}$$