Question 65280
The domain is the set of all real number, {{{ -infinity < x < +infinity }}}

y=x^2-2x+5
= x^2-2x+1 + 4
= (x-1)^2 + 4

y will always be greater or equal to 4.
Hence the range is  { y : y >= 4 }

{{{ graph(200,200,-4,5,-2,20, x^2-2x+5)}}}