Try also remove and reinsert the SIM card.
If it doesn't help visit your carrier, maybe the SIM card is damaged, ask for a replaced (new) card. Normally it is free.
Ask also to check if the SIM tray is bent, as even a tiny misalignment can cause the SIM card to not fully connect with the internal contacts in your iPhone.
Keep in mind: iPhone 5s is > 9 years old, which also affects the battery life. The hardware remains old, so does the battery.
👉 You should consider whether it is still worth replacing the battery, with the knowledge that you cannot update the iPhone 5s to a higher iOS.
👉 If you have an outdated iPhone that cannot be updated to iOS 13 or later, many apps will not be able to download.
Outdated iPhone no longer meets the requirements for many apps. Most apps required iOS 13.4 or later.
👉 Considering a newer type of iPhone?
Read this before you buy a newer type iPhone.
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If it is still possible, have the battery replaced.
The battery can be replaced by Apple or an Apple Authorized Service Provider.
See this Apple article: iPhone Battery Repair & Replacement - Apple Support
If you are going to replace the battery, see -> Get your iPhone, iPad, or iPod touch ready for service
Get your iPhone, iPad, or iPod touch ready for service - Apple Support
The price is approx $ 69.
If you want to know exactly, call Apple directly, see Contact Apple for support and service -> Contact Apple for support and service – Apple Support (UK)
or
call 1-800-MY-APPLE
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Thank you for your feedback and you're welcome.
