To solve the given expression:

5((4)/(7))/1((5)/(21))-(5((2)/(15))*((3)/(22))+1((14)/(15)))

First, simplify the division:

= 5 ((4)/(7)) / 1 ((5)/(21)) - (5 ((2)/(15)) ((3)/(22)) + 1 * ((14)/(15)))

= 5 (4/7) / (5/21) - (5 (2/15) * (3/22) + 14/15)

Next, evaluate each part:

= 20/7 / 5/21 - ((10/15) * (3/22) + 14/15)

= 20/7 / 5/21 - (2/3 * 3/22 + 14/15)

= 20/7 * 21/5 - (2/22 + 14/15)

= 420/35 - (1/11 + 14/15)

= 12 - (1/11 + 14/15)

Now, find a common denominator for the fractions:

= 12 - ((15/15) (1/11) + (11/11) (14/15))

= 12 - (15/165 + 14/165)

= 12 - 29/165

= 12 * 165/165 - 29/165

= 1980/165 - 29/165

Combine the fractions:

= (1980 - 29) / 165

= 1951/165

Therefore, the final answer is 1951/165.