To find the median and mode of the set of measurements \( \{5, 9, 3, 5, 8\} \), follow these steps:

Median Calculation

1. Sort the Data:
\[
\{3, 5, 5, 8, 9\}
\]

2. Find the Median:
- The median is the middle value in a sorted list.
- For the sorted list \(\{3, 5, 5, 8, 9\}\), the middle value is the third value.

\[
\text{Median} = 5
\]

Mode Calculation

1. Find the Mode:
- The mode is the value that occurs most frequently.
- In the sorted list \(\{3, 5, 5, 8, 9\}\), the number 5 appears most frequently (twice).

\[
\text{Mode} = 5
\]



So, the pair \((M, D)\), where \(M\) is the median and \(D\) is the mode, is \((5, 5)\).

D. (5, 5)