Envelope following using FFT bin power -> Low pass effect on the modulation transfer function
Any set of FFT framings of the data is a form of averaging filter or FIR filter, and thus will have a low-pass filtering effect over some envelope frequency range.  You can understand this effect by treating the FFT window as a FIR filter kernel and calculating its frequency response.

If the width of your FFT window is somewhere near the period of 5 Hz, then you will be in an area of filter roll-off.  You could try a shorter window, compensate for the window roll-off, perhaps using a "flat-top" window if your frequency of interest is well within the window's passband, or use another form of enveloper follower which does not have an intrinsic roll-off in the area of interest.