The front panel is attached with clips, and there are several ribbon cables connecting it to the rest of the phone. Your goal here is to release the clips and open the phone only enough to disconnect the cables. Go slowly and carefully to avoid damage.

Make sure the suction cup is firmly attached to the front panel assembly near the home button.

While holding the iPhone down with one hand, pull up on the suction cup to slightly separate the home button end of the front panel from the rear case.

With a plastic opening tool, gently pry the edges of the rear case down, away from the front panel assembly, while you pull up with the suction cup.

Take your time and apply firm, constant force. The 5s front panel assembly is a much tighter fit than most devices.