Your internal battery of Nexus 5 might be kaput and battery case might not also solve the case. If you don’t want to send your nexus 5 for a repair which might take some time, you can simply replace your battery yourself, even if it is non-removable.
Get the replacement battery for the Nexus 5 and little plastic tool to help you remove the original battery. You can buy Nexus 5 battery replacement tool from plenty of online sources. It usually should cost you up to 20 USD.
Nexus 5 Battery Replacement Procedure:
1. Turn off your phone. Use the plastic tool to remove the cover.
2. Remove the tiny screws and keep them at safe place.
3. Now remove the black plastic cover.
4. Now gently lever up the two little ribbons from the existing battery. Be gentle and they will both rise up.
5. Use the plastic tool to work around the battery to remove it from the device. Be calm don’t put useless force. After some work out the battery will come out.
6. Now put your replacement battery of Nexus 5 and put those two ribbons back as they were. Now place the black plastic cover back to its place and attach six screws back. Attach the original cover back and turn your phone on. That’s it you have replaced your Nexus 5 battery successfully.