**Core Concept**
The question is testing the understanding of calcium regulation in infants and the role of parathyroid hormone (PTH) in maintaining calcium homeostasis. In newborns, the parathyroid glands are immature, and PTH levels are usually low.

**Why the Correct Answer is Right**
The clinical scenario presented is a case of hypocalcemia (low serum calcium) in a 15-day-old infant. The low serum calcium level (5 mg/dL) and elevated phosphorus level (9 mg/dL) suggest a disorder of calcium-phosphorus metabolism. The elevated PTH level (30 pg/ml) indicates that the body is attempting to correct the low calcium level. However, in this age group, the parathyroid glands are immature, and the PTH response may be inappropriate or delayed. The most likely diagnosis is **Congenital Hypoparathyroidism**, which is characterized by low PTH levels and hypocalcemia due to underdeveloped parathyroid glands.

**Why Each Wrong Option is Incorrect**
* **Option A:** Pseudohypoparathyroidism is a rare genetic disorder characterized by resistance to PTH, leading to high PTH levels and hypocalcemia. However, in this case, the PTH level is elevated, not suppressed.
* **Option B:** Hypopituitarism can cause hypocalcemia due to decreased PTH secretion, but the PTH level in this case is elevated, not suppressed.
* **Option C:** Vitamin D deficiency can cause rickets and hypocalcemia, but the PTH level is elevated, not suppressed.

**Clinical Pearl / High-Yield Fact**
In infants and children, hypocalcemia can be caused by a variety of conditions, including congenital hypoparathyroidism, pseudohypoparathyroidism, and vitamin D deficiency. It's essential to consider the age of the patient and the PTH level when evaluating hypocalcemia.

**Correct Answer:** C.