Find the value of k in simplest form for which the larger root of x^2-5x+k=0 is x-5
did you mean that the larger root is x = 5 ?
(x-5) would be one of the factors.
then if f(x) = x^2 - 5x+ k
f(5) = 25 - 25 + k
= k
for x=5, f(5) must be zero, so k = 0
check:
you would have:
x^2 - 5x = 0
x(x-5) = 0
roots are 0 and 5, and sure enough 5 is the larger.