To solve the given expression, we can break it down step by step:

Step 1: Convert all mixed numbers to improper fractions
5 4/7 = 5 7 + 4 = 35 + 4 = 39/7
1 14/15 = 1 15 + 14 = 15 + 14 = 29/15

Step 2: Simplify the expression within the parentheses
5 2/15 = 5 * 15 + 2 = 75 + 2 = 77/15
Therefore, (5 2/15 • 3/22 + 1 14/15) = (77/15 • 3/22 + 29/15)

Step 3: Perform the multiplication and addition within the parentheses
(77/15 • 3/22) = (231/330) = (77/110)
Therefore, (77/15 • 3/22 + 29/15) = (77/110 + 29/15)

Step 4: Find a common denominator to add the fractions within the parentheses
(77/110 + 29/15) = ( (77/110) (3/3) + (29/15) (22/22) ) = (231/330 + 638/330) = (869/330)

Step 5: Subtract the result in parentheses from the initial expression
5 4/7 - 869/330 = 5 4/7 - 869/330 = (35/7) - (869/330) = (330/330) - (869/330) = (-539/330)

Therefore, the final answer is -539/330 or approximately -1.6303.