DIAGNOSIS This points to a battery communication failure or a bad connection, not necessarily a dead battery. The S5 has a smart BMS (Battery Management System) that can glitch.
FIX First, try a hard reset. Take the vacuum off the charger. Press and hold the power button for a solid 15-20 seconds. You're trying to drain any residual charge in the circuitry. Then, place it back on the charging dock. Wait for a solid white light on the dock, not a blinking one. Give it 15 minutes and try the power button again.
IF THAT DIDN'T WORK Remove the battery pack from the main unit (there's a button or latch on the battery itself). Check the metal contacts on both the battery and the vacuum for any debris or corrosion. Wipe them with a dry cloth, reseat the battery firmly, and try charging again.
HEADS UP Using third-party chargers or docks can confuse the smart charging system and lead to this. Stick with the OEM dock. If the battery is truly dead outside of warranty, you need the specific Tineco S5 replacement pack.