## **Core Concept**
The question assesses the developmental milestones of a baby, specifically focusing on motor skills such as reaching out and holding objects, holding the neck up, and sitting with or without support. These milestones are crucial in pediatric assessments to determine the developmental age of a child.

## **Why the Correct Answer is Right**
At around 4-5 months of age, babies typically develop the ability to reach out for and hold objects with both hands, a skill known as **prehension**. They also gain **neck control**, allowing them to hold their neck steady when their body is placed in a sitting or standing position. However, sitting without support usually develops a bit later, around 6-7 months of age. Therefore, a baby who can reach out and hold objects with both hands and hold their neck up but cannot sit without support is likely around **5 months** old developmentally.

## **Why Each Wrong Option is Incorrect**
- **Option A:** Typically corresponds to a younger age where these skills might not be present.
- **Option B:** Could be considered close but usually represents a stage slightly earlier or later depending on the exact milestones included.
- **Option D:** Represents an older age where the child would likely have achieved more advanced milestones, including sitting without support.

## **Clinical Pearl / High-Yield Fact**
A key developmental milestone to remember is that by **5 months**, infants should be able to **support their upper body with their arms** when on their stomach (often referred to as "tripod" position), **hold toys or objects**, and show **neck control**. However, the ability to **sit without support** usually emerges around **6-7 months**. These milestones help in assessing the neurological development of infants.

## **Correct Answer:** C. 5 months.