To add these numbers, we need to first convert the mixed numbers to improper fractions.

5 + (-4 1/3) + (-1 13/15)

Convert -4 1/3 to an improper fraction:
-4 1/3 = -4 + 1/3 = -12/3 + 1/3 = -11/3

Convert -1 13/15 to an improper fraction:
-1 13/15 = -1 + 13/15 = -15/15 + 13/15 = -2/15

Now, add the fractions:
5 + (-11/3) + (-2/15)

Common denominator for 3 and 15 is 15.
= 75/15 + (-55/15) + (-2/15)
= (75 - 55 - 2) / 15
= 18/15
= 1 3/15
= 1 1/5

Therefore, 2, 5+(-4 1/3)+(-1 13/15) = 1 1/5.