14 1 ( 519-538).38;

Решение:

$$\left(5\frac{14}{19} - 5\frac{1}{38}\right) \cdot 38 = \left(\frac{5 \cdot 19 + 14}{19} - \frac{5 \cdot 38 + 1}{38}\right) \cdot 38 = \left(\frac{95 + 14}{19} - \frac{190 + 1}{38}\right) \cdot 38 = \left(\frac{109}{19} - \frac{191}{38}\right) \cdot 38$$

Приведем дроби к общему знаменателю 38:

$$\left(\frac{109 \cdot 2}{19 \cdot 2} - \frac{191}{38}\right) \cdot 38 = \left(\frac{218}{38} - \frac{191}{38}\right) \cdot 38 = \frac{218 - 191}{38} \cdot 38 = \frac{27}{38} \cdot 38 = 27$$

Ответ: 27