So let's take this step by step. The only two numbers that will give you 5 is 1 and 5. The numbers that can give you 16 is 1, 2, 4, 8, 16. The whole idea behind factoring is playing with these numbers and seeing what gives you -38.
Let's set up the factors now:
(5r + __) (r - __)
What two numbers could you put in the blanks? If you multiply everything together, you'll have to get 5r^2-38r-16.
If you play around with the numbers, 2 and 8 could be used. So let's plug them in.
(5r + 2)(r - 8)
If you multiply them out, you'll get 5r^2 - 40r + 2r - 16, or 5r^2 - 38r -16. Hope that helps.