Find the next number in the series 13, 32, 57, 88, _____.

Let's find the difference between consecutive terms:
$$32-13=19$$

$$57-32=25$$

$$88-57=31$$

The sequence of differences is 19, 25, 31. Let's find the difference of these differences:

$$25-19=6$$

$$31-25=6$$

The differences increase by a constant value of 6. Thus, the next difference should be:

$$31+6=37$$

Therefore, the next number in the series will be:

$$88+37=125$$