Your iPhone 5s has sustained some damage, a component is malfunctioning or your battery appears to be dead. For whatever reason, you've decided to crack it open and repair it yourself. Before proceeding, consider your warranty. If it is still in force, no matter what your skill set, take it to your Apple store if possible.
What You Need
You need a suction cup with a handle or knob to pull the back off the chassis after you remove the retaining screws on the bottom panel on either side of the charger socket. Use a micro Phillips screwdriver or an eyeglass repair kit to do so. After removing the screws, place the suction cup on the back panel as near to the screws as possible while still maintaining suction. Lift up carefully and detach the charging plug from the socket before completely removing the back panel.
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When Inside Your iPhone 5s
Each of the interior components, including the battery, detach with the removal of various retaining screws. Tweezers come in handy for removal and replacement of all components. If you plan to reassemble your iPhone 5s, place each set of retaining screws in a labeled box or on a labeled sheet, as they vary in size and will not fit back into different slots. Replacement components are available from your Apple retailer.