Finding the Fourth Number: Maintaining Average in Sequence 5,7,3

To solve this problem, let's follow these concise steps:

• Step 1: Calculate the current average of the given numbers 5, 7, and 3.

The sum of the numbers is $5 + 7 + 3 = 15$.
The count of numbers is 3.
Thus, the average is $\frac{15}{3} = 5$.

• Step 2: Set up an equation with an additional number, $x$, so that the average remains the same.

Adding a fourth number, $x$, gives us a new set of numbers: 5, 7, 3, and $x$.
The new average should still be 5, so:

$\frac{5 + 7 + 3 + x}{4} = 5$

• **Step 3: Solve the equation for $x$.

Calculate the left side: $5 + 7 + 3 + x = 15 + x$.
Set up the equation: $\frac{15 + x}{4} = 5$.

Multiply both sides by 4 to eliminate the fraction: $15 + x = 20$.
Subtract 15 from both sides: $x = 20 - 15$, so $x = 5$.

Hence, the number that can be added without changing the average is $x = 5$.

Therefore, the correct choice from the provided options is option 3:

$5$