MJ.
You're not making any sense. Tell me please, how are you maintaining 5 degrees of bank into the live engine?
With aileron? Thought so. So there is more aileron available (control deflection) away from the live engine than into it. Thus, reduced authority to the live side. I think you'll find it rolls quicker to away from the live engine too.
I have, in 25 years of flying NEVER heard anyone advocate limiting turning bank angle to 5 degrees in an engine out situation.
I have however, heard much discussion of whether it is best to turn into or away from the live engine if there is a choice.