Question 5841
I am going to GUESS what you meant. I suspect that you did not use parenthese properly. If my guess is wrong, please submit the problem again.

{{{  f(x) = (2x-1)/(x-5)   }}}

Here's a graph (ignore the misbehavior around x=5, my graphing system is not great): 

{{{graph( 400, 400, -1, 10, -10, 10, (2x-1)/(x-5)) }}}

to find x-intercept, remember that x intercept means that the function is equal to zero. that's a simple equation:

*[invoke explain_simplification "(2x-1)/(x-5) = 0"]

so, 1/2 is the x intercept. Y intercept is the value of function with x set to zero, {{{-1/-5 = 1/5}}}

Asymptote is not a hard thing to find. You have two polynomials dividing one another, the asymptote is the fraction of the top highest coefficient to bottom highest coefficient, or 2/1, or 2. 

{{{(2x-1)/(x-5)}}} can be rewritten as 

{{{ (2x-1)/(x-5) = (2(x-5)+9)/(x-5) = 2 + 9/(x-5)}}}

the last part obviously is composed of two things, constant 2 and a part that approaches 0 as x tends to infinity. So 2 is the asymptote.