To simplify the given expression, we need to follow the order of operations: parentheses, exponents, multiplication and division, and finally addition and subtraction.

The expression given is:

( p^-1 p^5/4 ( p^-2/7 * q^1/4)^3,5)^-1

First, simplify the exponent inside the parentheses:

So, the expression becomes:
( p^-1 p^5/4 p^(-6/7) * q^(3/4))^5

Now, simplify the expression inside the parentheses:
p^-1 p^5/4 p^(-6/7) = p^((-1) + (5/4) + (-6/7)) = p^(3/28)

Therefore, the expression becomes:
( p^(3/28) * q^(3/4))^5

Next, apply the power rule for exponents:
( p^(3/28))^5 = p^(3/28 * 5) = p^(15/28)

( q^(3/4))^5 = q^(3/4 * 5) = q^(15/4)

Finally, the expression becomes:
p^(15/28) * q^(15/4)

Therefore, the simplified expression is:
p^(15/28) * q^(15/4)