#### Answer

$13\frac{17}{30}$

#### Work Step by Step

We combine the fractions by finding the LCD and simplify if necessary:
$5\displaystyle \frac{2}{5}+3\frac{7}{10}+4\frac{7}{15} =5\displaystyle \frac{12}{30}+3\frac{21}{30}+4\frac{14}{30} =12\displaystyle \frac{47}{30}=13\frac{17}{30}$