5" is an odd size. Can you tell us a little more about your existing pipe?
What is the pipe material?
Is this a butt weld system? Or a socket weld system?
Do you have a copy of the pipe spec for this line?
What does the existing pipe spec branch connection table call state? I wouldn't be surprised if they didn't for 5" NPS, but you could probably use the information from the 4" and 6" header size to make an assumption.
Yes, perpendicular branch connections are acceptable, and most times the norm. A 45 degree lateral connection may also be acceptable, dependent on a few factors. I'm not sure I fully understand your last question (should in project the branch pipe into the flow?).
Can you provide a sketch of the existing line for better visualization?