Is it worth upgrading from Apple Watch Series 5 due to rapid battery draining issue?

The Apple Watch lifespan is about 3-5 years, so it could be due for an upgrade. I don’t think the activity issues are related to the battery, the software and the lithium‑ion battery are usually not related when it comes to these software issues.

The battery could be losing charge quickly due to the capacity, is the battery capacity below 80%?

You can schedule a visit to see what’s going on with your watch though if you would like.

Apple Watch Service and Repair - Apple Support

Apple no longer services the Apple Watch 5, so you may have to buy a new Watch.

Buy Apple Watch - Apple

If the watch is telling you to get the battery serviced, you should either do that or stop using the watch. The battery may start to swell and push the crystal off the watch.

Apple considers devices obsolete at 5 years but all that means is that they don't provide support or repair. It doesn't mean that the device is no longer usable.

If you are considering purchasing a newer version of the watch in the fall, it may be worth springing for the replacement battery. The watch will then get you through until the newer versions are released and the initial furor dies down. In fact, the watch will probably still last you until past when it's getting watchOS updates. It will also mean the watch will have some resale value.

If you aren't planning on waiting, don't bother getting the battery replaced, just trade it in and get a new watch.

I suggest you upgrade your Watch, even if you invest about $100~ for a new battery, the Apple Watch Series 5 in general has aged a lot and soon will stop getting software updates soon. Even with the new battery, I don’t think its worth it investing in an old model Apple Watch.