Hey guys , Iv tuned my guitar to Eb

Im just wondering , Im playing my Harmonic Minor the the 5th fret ( Which is A in standard E )

But because iv tuned down to Eb will i start the Harmonic Minor on the 6th fret now ?
In Eb, the A Harmonic Minor will start on the 6th fret, yeah. Starting on the 5th fret is still harmonic minor, just G# harmonic minor, and not A.