Let's solve this step by step:

1. Given Information:

   • There are four number cards: 1, 4, and two unknowns (let's call them $x$ and $y$).
   • The median is 5.
   • The range is 13.

2. Understanding Median:

   • Since there are four cards, the median is the average of the second and third numbers when the cards are arranged in ascending order.
   • This means that $\frac{4 + x}{2} = 5$, which gives $4 + x = 10$ and $x = 6$.

3. Understanding Range:

   • The range is the difference between the largest and smallest numbers. The smallest number is 1, and the largest number must be $y$.
   • So, $y - 1 = 13$, which gives $y = 14$.

Thus, the missing numbers are $x = 6$ and $y = 14$.

The complete set of numbers is: $1, 4, 6,$ and $14$.

Would you like a detailed explanation or have any questions?

Here are 5 related questions:

1. How is the median calculated when there is an even number of data points?
2. How does changing the median affect the other numbers in a set?
3. Can you find the mean of the set $1, 4, 6, 14$?
4. What happens to the range if the largest number in the set changes?
5. How would the solution change if the range were a different number?

Tip: Always arrange data in ascending order when calculating the median and range.