iPhone 5s shows low battery symbol with lightning bolt when plugged in
The problem you're having is that the battery has most likely died and a battery replacement is in order.

An iPhone 5s battery is rated at having a life expectancy of 500 cycles. It's not uncommon for batteries to exceed or fall short of this number; it's just an estimation of how long it can last. In your case, though, the battery would have had a much longer than average life and, unfortunately, your attempt to calibrate the battery may have been the nail in its coffin.

The only thing to try (if you haven't already) is leaving it plugged in for a while to see if the battery starts getting a charge. You should know after about an hour (maybe earlier) if that's going to work.

Otherwise it really is the time for a new battery (or a new phone). Fortunately, if you want to have a go at replacing the battery yourself, this isn't too difficult for an iPhone 5s. See How to replace the battery in your iPhone 5s for more info.

However, most people would opt to have it replaced professionally or to upgrade their phone when it's this old as you don't know what other components may fail in the not-too-distant future.