The median of a list of 5 sorted numbers is the third (middle) number. For the median to remain unchanged, the position or value of the third number must not be altered.

Analysis of Each Option:
Option A: Multiply each number by 2
- Effect: All numbers are scaled by 2 , including the median.
- Result: The median changes (new median $=2 \times$ original median).
- Conclusion: Affects the median.

Option B: Add 10 to each number
- Effect: All numbers are increased by 10 , including the median.
- Result: The median changes (new median = original median + 10).
- Conclusion:

Affects the median.

Option C: Increase the largest number only
- Effect: Only the largest (5th) number increases. The middle (3rd) number remains unchanged.
- Result: The median stays the same.
- Conclusion: Does not affect the median.

Option D: Increase the smallest number only
- Effect: The smallest (1st) number increases. If it surpasses the original 2nd or 3rd number, the median may shift.
- Example:

Original list: $[1,2,3,4,5] \rightarrow$ Median $=3$.
New list after increasing 1 to $6:[2,3,4,5,6] \rightarrow$ Median $=4$.
- Result: The median can change.
- Conclusion:

Affects the median.

Option E: Decrease the smallest number only
- Effect: The smallest (1st) number decreases further. The middle (3rd) number remains unchanged.
- Result: The median stays the same.
- Conclusion: Does not affect the median.

Why Options C and E Are Correct:
- Option C (Increase largest number only): The median is determined by the 3rd number, which is unaffected by changes to the largest number.
- Option E (Decrease smallest number only): Similarly, decreasing the smallest number does not alter the 3rd number.

Final Answer:
The operations that do not affect the median are:

C and E