[tex]13\frac{1}{7}-5\frac{5}{21}=13\frac{3}{21}-5\frac{5}{21}=(13-5)+\left(\frac{3}{21}-\frac{5}{21}\right)\\\\=8-\frac{2}{21}=\left(7+\frac{21}{21}\right)-\frac{2}{21}\\\\=7+\frac{21-2}{21}=7\frac{19}{21}[/tex]
The appropriate choice is ...
... D. 7 19/21