An error is either:
1. A real bug someone ran in to.
2. Not a bug and just a spurious "error", which should be a log message, some statistic somewhere, or just disabled outright. Errors should only be errors – an uncaught exception, explicit error log, stuff like that. Everything else should be something else.
What I've found – and this certainly won't hold true for all cases, but it does seem to be the case often – is that half or more all in the second category: it's just stuff that shouldn't be logged as an error. This is usually trivial to fix.
This still leaves you with 5,000 errors/day, but typically ~10 bugs will cause ~4,950 of them. This takes more time to fix, depending on the bug, but usually also takes less time than "5,000 errors every day!" makes it sound.
The last ~50 errors are usually the hardest, especially if it's frontend JavaScript stuff. I "read every error", but I have a few that pop up regularly that I just can't reproduce and don't know how to fix. I think it may be extensions people use or something, but idk. Since this post talks about APIs I guess that's not really applicable to them.