LTspice gives wrong AC analysis
As mentioned by just about everyone in the comments, your op amp doesn't work because your DC bias point is 0V and the op amp will only work for inputs between its rails (0V and 5V).

Your options are either:
1) Use positive and negative op amp rails, or
2) Bias the input AC voltage to between the two rails, e.g. 2.5VDC.

As seen below, with the DC bias point set at 0, I get similar broken behavior (although its a bit different since I used a different op amp)



If I add a 2.5V DC offset to the AC input, I get the expected behavior:



EDIT:  See also The Photon's answer describing why the minimum output voltage limits you in this case.