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)