The sum of -2 9/10 and -5 4/15 is -7 1/6. When we convert these fractions into improper fractions, they become -29/10 and -64/15. Now, we must make the denominator of each fraction equal to one another. Therefore, we must multiply -29/10 x 3 and -64/15 x 2 to get the denominator the same. The final answer is 215/30 which simplified is -7 1/6.