How long will a 500 Wh power station run a led tv (50")?

Short answer: about 5 hours. The math: 500 Wh rated × 0.85 inverter efficiency = 425 Wh delivered, ÷ 90 W average draw = 4.7 hours.

Runtime at a glance

Battery stateUsable energyRuntime
New battery425 Wh5 h
~2 years old (80%)340 Wh4 h
~4 years old (60%)255 Wh3 h
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Quick answers

Why multiply by 0.85?
Converting DC battery power to AC wall power loses roughly 15% in the inverter. Manufacturers quote the battery's rated Wh, not what reaches your appliance.
What shortens the runtime?
Battery age (−20% per ~2 years), cold weather, and the display/inverter idle draw on small loads. Treat 5 hours as a good-conditions estimate; plan on ~4 for an older unit.
What if I run other things at the same time?
Runtime divides across loads: add a 12 W router and the same battery lasts about 4 hours instead.