Hey, gpiphoto.
After reviewing your post, it appears you're no longer receiving notifications for an Xfinity application you have installed on your iPhone 5s since updating to iOS 11. Good job in contacting Xfinity about this issue and I'm happy to help.
- Use notifications on your iPhone, iPad, and iPod touch -- Turn off notifications for whichever Xfinity application isn't working correctly.
- Force an app to close on your iPhone, iPad, or iPod touch -- Force close the Settings application and the Xfinity application if it's open.
- Restart your iPhone, iPad, or iPod touch -- Then, restart your iPhone. Once it's returned to the Home screen, re-enable notifications for the Xfinity app and test the issue.
How to back up your iPhone, iPad, and iPod touch -- If restarting your phone after turning off the Notification for that application and forcing the application closed didn't resolve the issue, please be sure to have a fresh backup to keep your personal information safe. In order to back up your Health data, the backup needs to be encrypted. iCloud does this automatically, but iTunes doesn't. If you'd like to use iTunes to back up your phone, refer to this article: About encrypted backups in iTunes
How to check the storage on your iPhone, iPad, and iPod touch -- Even though the title of this article doesn't directly apply to your issue, there's a step included that can help. Offload the Xfinity application but retain the data on your phone by going to "Settings > General > [Device] Storage". Restart your phone once again. Once your iPhone returns to the Home screen, return to "Settings > General > [Device] Storage" and reinstall the application from the the same location.
Depending on the app, you might be able to delete some of its content, or delete the app and all of its content. You can also offload the app, which frees up storage used by the app, but keeps its documents and data on your device.
Let me know how that goes.
Take care!