(b) Given $$ f(x)=\frac{-4}{x-p}+q $$ (1) If the asymptotes of $$ f $$ intersect at the point ( $$ 5 ; 1 $$ ), determine the values of $$ p $$ and $$ q $$.

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To find the values of $$ p $$ and $$ q $$ for the function $$ f(x) = \frac{-4}{x - p} + q $$, we need to identify the vertical and horizontal asymptotes of the function.

1. **Vertical Asymptote**: The vertical asymptote occurs where the denominator is zero. Thus, we set $$ x - p = 0 $$:
   $$
   x = p
   $$
   Therefore, the vertical asymptote is at $$ x = p $$.

2. **Horizontal Asymptote**: The horizontal asymptote can be found by analyzing the behavior of $$ f(x) $$ as $$ x $$ approaches infinity. As $$ x \to \infty $$, the term $$ \frac{-4}{x - p} $$ approaches $$ 0 $$. Thus, the horizontal asymptote is:
   $$
   y = q
   $$

Given that the asymptotes intersect at the point $$ (5, 1) $$, we can set up the following equations based on the coordinates of the intersection:

- The vertical asymptote $$ x = p $$ intersects at $$ x = 5 $$:
  $$
  p = 5
  $$

- The horizontal asymptote $$ y = q $$ intersects at $$ y = 1 $$:
  $$
  q = 1
  $$

Thus, the values of $$ p $$ and $$ q $$ are:
$$
\boxed{(5, 1)}
$$
The values of $$ p $$ and $$ q $$ are $$ (5, 1) $$.

(b) Given
(1) If the asymptotes of intersect at the point ( ), determine the
values of and .

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(b) Given (1) If the asymptotes of intersect at the point ( ), determine the values of and .