I need to cut 5" x 30" out of a basement support beam to accommodate a door and secondary suite height requirements. Would the jack and king posts for the door be enough support for the 5"x30" or do I need to put in 6"x6" posts? footings?
If you really have an 8"x10" beam in your basement it is probably supporting a huge amount of weight. Please do not even consider cutting into it without getting an engineer to determine what kind of supporting columns are required. (Cutting away 50% of the depth will reduce the strength by 75%.) I am guessing that in addition to the columns you will need to add footings to avoid punching through the floor, but those kinds of questions depend on exactly how your foundation is built. ("Code requirements" would depend on your location but major structural work like this would almost certainly require a permit and inspection. But frankly the safety ramifications of undermining the house's structure are probably more important.)
In short, this is an enormous project. Is there nowhere else to put the door?
You need to get an engineer involved to do some calculations.
Options (with an engineer's sign-off) would seem to include pouring some footings and installing steel pipe or I beams for your columns, or building up rebar-reinforced masonry columns. You could face those with brick or stone (or wood) and have something really nice looking.
I wouldn't think standard door framing would be sufficient to replace the load you're transferring to the posts, and I would definitely think you need to pour footings under the columns.
If you notch either edge of that beam anywhere along the length of the beam, whether it's a couple of inches or 30 inches, you really have to consider that you have reduced the effective dimension of the beam by the depth of the cut.
If you cut a 5" notch out of a 10" beam, you have turned the entire open span into a 5" beam. If the beam is 8" wide, I would have to think that the weight of the beam alone would stand a good chance of breaking the beam (without appropriate columnar supports).
One option might be to replace the beam with a steel I beam, which would give you the extra headroom you're looking for without compromising the strength of the beam. Yes, I know how big of a job that sounds like, but that should be a hint about how big a job this actually is and how badly it could go wrong.