To calculate this expression, we first need to simplify the terms within the parentheses, then perform the remaining operations.

Step 1: Simplifying the terms within the parentheses
5 3/10 = 53/10
3 4/5 = 19/5

(53/10 - 19/5 13/38) 5/84 + 2 1/8

Step 2: Perform the multiplication and subtraction within the parentheses

(53/10 - (19/5 13/38))
= (53/10 - (247/190))
= (53/10 - 247/190)
= (19053 - 10247) / (10190)
= (10070 - 2470) / 190
= 7600 / 190
= 40

Now we have:

40 * 5/84 + 2 1/8

Step 3: Perform the multiplication
40 * 5/84 = 200/84 = 25/21

Now we have:

25/21 + 2 1/8

Step 4: Convert the mixed number to an improper fraction
2 1/8 = 16/8 + 1/8 = 17/8

Now we have:

25/21 + 17/8

Step 5: Find a common denominator and add the fractions
To find a common denominator, we multiply 21 and 8 which gives us 168.

(25/21)(8/8) + (17/8)(21/21)
= 200/168 + 357/168
= 557/168

Therefore, the final result is 557/168 or approximately 3.3155.