How does Unyielding Spirit interact with Glowstone triggered ability?

Yes — Unyielding Spirit prevents the 5 damage from Glowstone's end-of-turn trigger. Glowstone itself still dies.

Glowstone's trigger ("At the end of your turn, kill this and deal 5 to all units you control") deals damage directly from the ability — the ability is the source of that damage (Rule 417.6.b.2). That's "ability damage," so the global prevention from Unyielding Spirit ("Prevent all spell and ability damage this turn") stops it, even if Unyielding Spirit is played in reaction to the trigger.

This is different from fight effects like Challenge, where the units deal the damage and Unyielding Spirit does nothing. The "kill this" instruction is not damage, so Glowstone is still killed by its own trigger.