A 5 Axis Machining center is a form of a milling machine used to remove material from a piece of stock in a very precise manner controlled to computers (CNC - computer numerical control). Traditional milling machines have 3 axes of motion. The axes are called X Y and Z based on the Cartesian coordinate system. A 5 Axis Machine has 2 additional axes of motion, typically called the A and B axes. The A and B axes are rotary and allow the endmill (milling cutter) to reach areas not possible with a 3 Axis Machine, machine features that would require additional operations on a 3 axis machine and machine features that have a swarf or transition.
5 Axis Machining is most prevalent in the aerospace industry where the parts tend to not be prismatic. 5 Axis Machining is also used in die making, mold making and for producing parts where holes or features are an angles that require multiple setups.
As with designing any part the key is to keep it as simple as possible to allow the part to perform it's intended function. The more prismatic a part is and the more it's features are parallel and perpendicular the easier it is to machine. If you design parts and can't avoid off angle and swarfing features try to keep as many of the features on the same plane as possible, make sure there is adequate room for an endmill or other cutter to access the areas to be machined and give consideration as to how the part with be held in the machine during the machining operation. And always be mindful of the tolerances you specify on the part to make sure they are realistic.
5 Axis Machining is complex and requires a lot of expertise and investment in machine tools and CAM software. As such, 5 axis machined parts will typically be more costly that sourcing parts that can be made on traditional 3 axis machines. The factors that will determine price are the size of the part, the tolerances, the material as well as the number and complexity of geometric features.