this is an egg safety question

here's what I did:

1. in a double boiler dissolve 150g powdered sugar in juice of 1-1/2 lemons

2. add white of one egg and cook until it reaches 160F, stirring constantly

only thing is, I don't have a thermometer so I just guessed and cooked it
for ~5 min after adding the egg whites

does that sound sufficient? I hope so...