To determine the total kilograms of paper recycled after 5 weeks, you can substitute the value of \( w \) (the number of weeks) into the equation \( p = w + 9 \).
Given:
- \( w = 5 \)
Substituting into the equation:
\[ p = 5 + 9 \]
Calculating this gives:
\[ p = 14 \]
Therefore, after 5 weeks, Edwin's office will have recycled 14 kilograms of paper.