The brief records of the scores from highest to lowest are: +10, +8, 0, -3, -5. Since Xiao Ming ranked third and scored 90 points, the brief records are based on Xiao Ming's score as the standard. First, we calculate the scores of each student, and then we calculate the average score of these 5 students.

This question examines the application of rational numbers in real life. Determining Xiao Ming's score based on his score and ranking third is key.

Let's calculate the scores of each student:
- The student with +10 scored $90 + 10 = 100$ points.
- The student with +8 scored $90 + 8 = 98$ points.
- Xiao Ming scored $90$ points.
- The student with -3 scored $90 - 3 = 87$ points.
- The student with -5 scored $90 - 5 = 85$ points.

To calculate the average score of these 5 students:
$$\text{Average} = \frac{100 + 98 + 90 + 87 + 85}{5} = \frac{460}{5} = 92$$

Therefore, the average score of these 5 students is $\boxed{92}$.