Though I don't want to over-simplify this sophisticated type of equipment, there are only two types of five axis machining applications (in very general terms).
First, many companies must simply expose different surfaces (planes) to the spindle for machining. Such would be the case on a very odd shaped workpiece that must be machined on several sides. In one sense, this kind of machining is simply an extension of what can be done with the fourth axis. If this is your area of interest, you'll want to learn more about "variable plane selection". This feature is like the standard G17, G18, and G19 (XY, XZ, YZ) plane selection commands, but it allows you to define any plane for machining. This allows you to use many of the standard programming features like canned cycles, cutter radius compensation, and axis rotation, making programming much easier.
Second (and the more classic type), when machining elaborate 3d shapes, as would be the case with injection molds and edm electrodes, it is important to keep the cutting tool perpendicular to the machined surface during machining. This requires five axes of motion (three linear, two rotary). Note that this kind of machining is always so sophisticated that it requires a cam system to prepare programs, and the cam system does all the hard work related to figuring out the axis motions.
When it comes to how the additional two axis are actually handled on the machine, again there are only two ways. First, with smaller machines, the rotary axes are commonly handled with rotary tables. The workpiece is rotated to achieve which ever type of five axis machining you're doing. Note that this kind of machine is especially suited to the first type mentioned above, since there are no limitations to rotation (full 360 degrees in both rotary axes), and many surfaces can be exposed for machining.
Second, when the machine becomes so large that it is infeasible to rotate the workpiece (as is the case with gantry mills), the two rotary axes are incorporated into the machine's headstock. The tool actually tilts in two directions. There will always be a limitation to how much the tool can tilt, which also tends to limit the application for this kind of machine to 3d work.
Frankly speaking, there's not that much more to five axis machining. Again, you'd need to look into variable plane selection if you will be doing the first type of five axis work, but I know of no other major topics for discussion. If anyone has more information to relate, we welcome your comments.
