Would I have died or would I have 1 life remaining.
You would have 1 life remaining. Action order:
- Opponent casts Beacon of Destruction, it goes on stack.
- Sunscorch Regent triggers, it goes on stack.
If both players pass, the stack starts resolving top to bottom. First you gain 1 life and put a counter on Regent. You now have 6 life. Next, Beacon resolves, you are dealt 5 damage and now have 1 life.
Remember that the last to trigger is the first to resolve. Your opponent will have played a spell which will trigger your dragons ability and then when things start resolving you will gain a life and put a counter on before the spell that triggered your dragon gets a chance to resolve.