The function
\[
\sqrt{x^{2}+10 x+11}-x
\]
has one horizontal asymptote at $y=$

Step 1 ：The function given is \(\sqrt{x^{2}+10 x+11}-x\).

Step 2 ：The horizontal asymptote of a function is the value that the function approaches as x approaches infinity or negative infinity.

Step 3 ：We need to find the limit of the function as x approaches infinity and negative infinity.

Step 4 ：If the limits are the same, then that is the horizontal asymptote. If they are different, then the function has two horizontal asymptotes.

Step 5 ：The limit of the function as x approaches infinity is 5 and as x approaches negative infinity is infinity.

Step 6 ：Therefore, the function has one horizontal asymptote at y = 5.

Step 7 ：Final Answer: The horizontal asymptote of the function is at \(y = \boxed{5}\).