If Arsenal finished fifth and won the Champions League, sixth would also qualify. That obviously won't be happening, though.
We qualify for Champions League if we finish top five and/or win this year's competition.
We qualify for Europa League if we win the FA Cup or finish sixth. Or if we finish seventh and the FA Cup winner finish in the top six.
We qualify for Conference League if Newcastle qualify for the Champions League or Europa League and we finish seventh (eighth if FA Cup winners finish top seven).
We could also qualify for Conference League by finishing ninth if Newcastle qualify for Champions League or Europa League and Chelsea finish eighth and win this year's Conference League.
There, simple.
There are other theoretical ways of qualifying but would involve Arsenal basically losing every league game so they drop out of the top four and winning the Champions League, or Man U or Tottenham pretty much winning every league game so they finish in the top seven or eight and then also winning the Europa League, so not very likely.