code approved way to cut 5"x30" out of a 8" x 10" support beam
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?