I have searched and searched, but not been able to find the correct method to answer this kind of question:

"How much would you have to invest today in order to receive USD 5000 each year for 10 years, at an interest rate of 8%.

I would be very grateful for an example on how to solve this kind of question.

Paraphrasing, "What amount A would have to be deposited into an account that earns 8% per year on the invested balance, such that one could withdraw $5,000 per year for 10 years (at the end of each year), and such that the final withdrawal would exactly empty out the account?"

This type of scenario has a nice closed-form solution, given by the formula

A \ = \ w \ \times \ \frac{1-\frac{1}{(1+r)^n}}{r}

In your case, the roles of the annual withdrawal w, the interest rate r, and the number of years n, are being played by 5,000; 0.08; and 10; respectively. Give that a spin.