To find out what score you need on the fifth test to achieve an average of 83%, we can follow these steps:

1. Let the score you need on the fifth test be represented by $x$.

2. To find the average, we add up all five test scores and divide by 5. The equation for the average is: $\frac{80 + 75 + 90 + 86 + x}{5} = 83$

3. Multiply both sides of the equation by 5 to eliminate the denominator: $80 + 75 + 90 + 86 + x = 415$

4. Add up the scores from the first four tests: $80 + 75 + 90 + 86 = 331$

5. Substitute this into the equation: $331 + x = 415$

6. Solve for $x$: $x = 415 - 331 = 84$

So, you need to score 84% on the fifth test to achieve an average of 83%.

Do you want more details or have any questions?

Here are 5 related questions to expand on this:

1. How does the concept of weighted averages differ from simple averages?
2. What would happen if the average needed was higher than 83%?
3. How does scoring below the required average on a test affect the overall average?
4. How can you calculate the average of multiple tests if the scores are given in fractions instead of percentages?
5. What is the impact of a zero score on one test when calculating averages?

Tip: When calculating averages, make sure to sum all elements before dividing by the total number of elements.