[Ryland]

Originally Posted by S-F

why does my furnace have 5 terminals?

Your link explains why.

Terminal designations
The usual terminals are:
G – Fan, usually a green wire
R – 24 VAC usually a red wire (Rc an Rh are discussed later)
C – 24 VAC Common
Y – Compressor, usually a yellow wire
W – Heat, usually a white wire
The thermostat is a set of contacts where G, W and Y are connected to R based on the following rules.
Cooling
If there is a call for cool, R is connected to Y (compressor). In air conditioning mode the thermostat controls the fan, so G (Fan) is also connected to R. For cooling, the furnace usually selects the high speed of the blower.
[edit] Heating
In conventional heating which is oil or gas, the furnace controls the fan, so only R is connected to W (heat). For electric heating, the thermostat controls the fan (G), thus in this case both G (Fan) and W (heat) are connected to R (24 VAC). For heating applications, a lower blower speed is used and the furnace selects it.
The furnace controls the fan because oil and gas heat is not instantaneous. In order to avoid a blast of cold air, the furnace controls the fan. It can do this with a simple delay or by temperature set by the limit switch in the plenum.
Humidification
Humidification is a heat only function. Humidifiers are controlled by the W (heat) terminal.
Rc, Rh and R
Rc and Rh have been added to accommodate separate transformers for heating and cooling, thus for single transformer systems Rc and Rh are jumpered together and assume the function of the R terminal. Some systems use R and Rc, so consider R to be Rh in this case. Rh is defined as R (heating) and Rc is defined as R (cooling).
The Fan (G) terminal
The Fan (G) terminal is usually connected to Rc when Rc exists on the thermostat.
The Common terminal
The common terminal has been a recent addition because early thermostats created the switches with the liquid metal mercury. Mercury is a hazardous material and must be disposed of properly. Electronic thermostats need power to operate and it would like both a hot and a common terminal to get power or both ends of the transformer secondary need to be available to the thermostat.
There is a technology called “power stealing” where unopened switches can power thermostat. The current available is limited by the resistance of the furnace relays.
Power can also be provided by a set of batteries. When the batteries die, you then have no air conditioning or heating.

And it's done this way because if you have Air conditioning in your house it's often hooked up to the furnace, also if you have a wood stove but want the air in your house filtered and circulated so that the heat is distributed around your house then you turn your thermostat to "fan".