I think before we get to this answer we need to understand how roots of a quadratic equation works.
When a quadratic equation have 2 real roots such as a/b and c/d we can write the quadratic equation in factored form like this y or 0=(bx-a)(dx-c)
In this case we know the 2 roots are 5 and 2/3 and one of the factors is already x-5. so the other one according to the equation above that I wrote have to be 3x-2 and therefore the 3rd choice is correct.
Hope this helped you and if there is any questions about this please let me know in the comments.