So far, I see only bits and pieces of correctness here
There are two things at work in a jet but before I get to that let me first talk a bit about the 5° bank into the good engine thing.
The reason you would do this is to help with rudder effectiveness and to reduce drag. It comes from the Vmca certification rules in either Part 23 or Part 25. It does not necessarily have anything to do with single engine performance, but rather with single engine loss of control. I have flown plenty of turboprops in which it is not at all necessary to bank 5° into the good engine to achieve satisfactory or even optimal performance in an engine-out situation.
Having said that, there may well be some performance advantages to banking into the operative engine in the event of an engine failure. Given that a Part 25 certified airplane must climb to certain specifications after the loss of an engine, the act of banking 5° into the operative engine might indeed be required to achieve the minimum, required performance. In other words, if the AFM says to do it then you should do it because it is a tested and accepted pilot technique applicable to the situation. Otherwise I would argue that you needn't gratuitously offer 5° of bank in any single-engine situation just because that's what you did in a Duchess or a Seminole.
Now, in a swept wing jet things are a bit different. The two things I alluded to above are important to understand if you are, or are about to start, flying one. First, the sweep of the wing plays a role that is best described graphically but I shall atempt to describe it verbally.
When an engine fails that airplane yaws, right? Let's just say that you're observing from the top of a 737 when the right engine fails. The airplane yaws to the right, correct? Where do the wings go? The wing with the failed engine on it moves aft or, retreats, while the wing with the operating engine moves forward or, advances. The airplane however, continues to fly more or less straight ahead. It might roll without corrective action, but it flies straight ahead.
Now let's take a look at that advanced wing. Get out your CFI model if you have to in order to understand this. The advanced wing now has air flowing over it in a way that was not intended when the wing was designed. Effectively the chord of the wing is now longer and hence the amount of lift generated by it is greater. Now, you might say that the same thing is true about the other wing but the situation is a bit different in that the advanced wing receives uninterrupted ariflow while the retreated wing does not. The end result is that the advanced wing produces more lift and induces more roll in this crabbed orientation than if the airplane were held straight with the rudder (ball in the middle).
Putting the ball in the middle puts the airplane back in a straight-ahead flying condition that puts both wings where they should be in terms of airflow and lift balance. The airplane will actually fly a bit better if you keep the plane straight with the rudder than if you don't.
Now, moving on to the other issue that you probably have to consider (definitely in any Boeing), we need to talk about spoliers. If the airplane in question has roll assist spoilers (737, Gulfstreams, etc.) you will engender their operation automatically by using the aileron controls. You won't be able to prevent it. Roll spoliers assist the ailerons by destroying lift on the wing that is directed downward when the ailerons are deflected. If the boards are up, they're taking away from the overall lift that the airplane is producing.
Allowing the ball to remain un-centered will mean that partial roll control must be maintained by using the ailerons. This will, at some point, possibly from the moment you add aileron, raise some or all of the spoilers on one wing, destroying some of the lift and increasing the total drag on the plane. That's hardly a recipe for better performance in a single-engine situation.
Applying enough rudder to straighten out the longitudinal axis of the airplane solves this problem by eliminating the rolling moment with the rudder instead of the ailerons and roll spoilers. Your wing stays cleaner and so do your shorts!
The bottom line is that 5° of bank is basically inappropriate unless the AFM or POH says that's what you should do in response to an engine failure, despite whatever you may have learned growing up.
TIS
