First, simplify the expression within the parentheses:

3 1/3 + 51/6 = 10/3 + 51/6
Convert 3 to 9/3 to have a common denominator:
10/3 + 51/6 = 30/9 + 51/6
Now, find a common denominator:
30/9 + 51/6 = 20/6 + 51/6
Combine the fractions:
20/6 + 51/6 = 71/6

Now, multiply the result by 2/5:
71/6 2/5
= (712) / (6*5)
= 142 / 30
= 71 / 15

Finally, subtract 23/5 from the result:
71/15 - 23/5
Convert 71/15 to have a common denominator:
71/15 - 23/5 = 71/15 - 69/15
Subtract the fractions:
71/15 - 69/15 = 2/15

Therefore, the final answer is 2/15.