Depending on who you ask, there are somewhere between three and seven simple machines. Since the title of this article is for five, here's the traditional five machine list:
(2) Inclined plane
(3) Wheel and axle
(4) Wedge (not always counted)
(5) Screw (not always counted)
If you're wondering what six and seven might sometimes be, add in the following:
(6) Pulley (just a different application of the wheel and axle)
(7) Gear (a wheel and axle with wedges around it can count as a compound machine)
The LEVER is used to alter the force needed to do work. It is generally a lengthy rod of some sort that pivots at some point, which is called a fulcrum. The force required is inversely proportional to the distance from the fulcrum, so a lever can be used to lift heavy objects when the object is near the fulcrum and the user is further out along the lever. The lever can also be used to reverse the direction of a force, as with a see-saw on a classic playground (now forbidden on modern playscapes).
The INCLINED PLANE is just what it says a flat surface set at an angle to some other surface. The inclined plane, such as a wheelchair ramp, works by applying a perpendicular force against any object that pushes against it. The sum of the force applied by the ramp and the other forces moving the object add up to result in a force in a different direction. The wheelchair that was being pushed forward, for example, is redirected upwards by the inclined plane.
The WHEEL AND AXLE is exactly what it sounds like. The wheel has a larger radius than the axle, but they are attached so that they must rotate together. As with the lever, the force required is less when the distance from the center of the axle is greater. Your car exerts a large force on the axle in order to turn the wheels very quickly. You easily turn the door knob a much greater distance than the central rod turns because trying to grasp and turn the narrow rod itself is more difficult and requires more effort to turn directly.
The WEDGE can actually be regarded as a pair of inclined planes. The major difference is that in most applications, the wedge moves, whereas the traditional inclined plane remains stationary. The basic idea behind a wedge is that as it is forced into an object, it exerts forces outwards, splitting the object. Axes, knives, razorsany cutting surface is a wedge. The front of a boat also behaves as a wedge, forcing the water to either side of the boat.
The SCREW converts between rotational and linear forces. If a screw is turned (a rotational force) the threads force the screw to move forward or backward. Conversely, if the screw is pushed or pulled with sufficient force, the threads will cause the screw to rotate as it slides. Some people will look upon the screw as a combination of a wheel and axle and an inclined plane (or wedge). There is nothing wrong with this view, but most people still regard it as one of the simple machines.
As for the other two:
The PULLEY is a special application of the wheel and axle, used to redirect applied forces. (i.e. You pull down on a rope to lift an object up.) Because the pulley's axle is often not involved directly, except to hold the pulley in place, people sometimes choose to distinguish the pulley as a separate machine.
The GEAR is a combination of a wheel and axle and wedges, used to transfer forces (generally to other gears). Because there is no actual splitting going on, some people prefer not to consider the teeth on gears as wedges, and name the gear as a separate simple machine.
If you are still learning (or want to teach new learners) about simple machines, there is a delightful interactive website which deals with all seven, and goes on to introduce the concept of compound machines. If you're bored and like silly robots, I recommend that you try it out.