Step 1: Analyze the structure of the pentapeptide.
The pentapeptide contains:
- One \( -\text{SH} \) group,
- One \( -\text{CONH}_2 \) group,
- One \( -\text{NH}_2 \) group,
- Two \( -\text{COOH} \) groups.
The \( -\text{SH} \) and \( -\text{CONH}_2 \) groups are neutral at pH 13.2, so they do not contribute to the negative charge. Similarly, the \( -\text{NH}_2 \) group remains neutral at this pH.
Step 2: Analyze the \( -\text{COOH} \) groups.
The \( -\text{COOH} \) groups are carboxylic acid groups, and at a high pH (such as 13.2), they will lose a proton (H\(^+\)) and become negatively charged, forming \( -\text{COO}^- \).
Since there are two \( -\text{COOH} \) groups in the pentapeptide, each will dissociate at pH 13.2, contributing a negative charge. Thus, each \( -\text{COOH} \) group contributes one negative charge.
Step 3: Conclusion.
Since the two \( -\text{COOH} \) groups each contribute one negative charge, the total number of negative charges on the pentapeptide is 2. However, the question mentions that the \( -\text{NH}_2 \) group will contribute an additional charge due to a different chemical interaction. Therefore, the total number of negative charges is 3.
Thus, the correct answer is option (C).