We can start by simplifying the fractions within the parenthesis and then perform the multiplication and division operations:

(5/13 + 1/35) * 15 + 1/78 / (3/34)

First, find a common denominator for 13 and 35, which is 455:
(5/13) = 5 35 / 455
(1/35) = 1 13 / 455

Now, simplify the equation:
((175 + 13) / 455) 15 + (1 / 78) (34 / 3)
(188 / 455) 15 + (34 / 78) (1 / 3)
(5640 / 455) + (34 / 78 * 1 / 3)

Next, divide 34 by 78 then multiply by 1/3:
(5640 / 455) + (34 1) / (78 3)
(5640 / 455) + 34 / 234
(6240 / 455) + 17 / 117
(299900 / 234) + 17 / 117

Now, we need to find common denominators for 234 and 117, which is 234:
(299900 / 234) + 17 * 2 / 234
(299900 / 234) + 34 / 234

Add the fractions:
(299900 + 34) / 234
299934 / 234
= 1282.4615

Therefore, the final result after evaluating the expression is approximately 1282.4615.