To add 7 5/19 and 3 7/29:

7 5/19 = (7 * 19 + 5) / 19 = (133 + 5) / 19 = 138 / 19

3 7/29 = (3 * 29 + 7) / 29 = (87 + 7) / 29 = 94 / 29

Now, add the two fractions:

138 / 19 + 94 / 29

To find a common denominator, we can calculate the least common multiple (LCM) of 19 and 29, which is 551.

Now, convert the fractions to have a common denominator of 551:

(138 29) / (19 29) + (94 19) / (29 19)
= 4002 / 551 + 1786 / 551
= 5788 / 551

Convert the improper fraction back to a mixed number:

5788 ÷ 551 = 10 with a remainder of 238
So, 5788 / 551 = 10 + 238 / 551 = 10 238/551

Now, subtract 4 5/19 from 10 238/551:

10 238/551 - 4 5/19
= 10 + 238/551 - 4 - 5/19
= 6 + 238/551 - 5/19
= 6 + (238 19 - 5 551) / (551 * 19)
= 6 + (4522 - 2755) / 10469
= 6 + 1767 / 10469

Therefore, the final answer is 6 1767/10469.