Using Common-mode choke as inductor
This is just a stab in the dark pointer that hopefully indicates the size of inductor core needed....

A good permeability ferrite core might have an inductance of 10 uH for one turn and, to get 1 mH you need 31 turns because inductance is proportional to turns squared.

So, with 5A RMS the peak current is about 7.1 amps and that's an MMF (magneto motive force) of 219 amp-turns. Given that the mean length around a fairly sizable ferrite is about 40 mm, the H field (amp-turns per metre) is going to be 5480.

If the relative permeability of the core is about 3000 and remembering that µ0 = 4π × 10^−7, the resultant flux density will be 5480 x 3000 x µ0 = 21 tesla and too much for a ferrite (and also iron) core of the mean length mentioned above. Ferrite starts to saturate generally at about 300 mT.

So, get looking for something that is quite large - nothing ferrite will work as far as I know - it will probably need to be laminated iron and the size of a small transformer. Something you could comfortably hold in the palm of your hand and would weigh about half a kg (maybe a tad less).