There are a number of misconceptions about 2.4 GHz and 5 GHz Wi-Fi. Let's clear those up.
Speed
In the US, the FCC set aside the frequencies 2,400-2,483.5 MHz and 5,150-5,725 MHz for unlicensed broadcasts such as Wi-Fi, cordless phones, etc.* These regions are known as the 2.4 GHz and 5GHz bands, respectively.
The upper frequency of a band minus the lower frequency of a band is the "bandwidth". The bandwidth of a frequency band is directly proportional to the rate at which data can be transmitted. The bandwidth of the 2.4 GHz band is about 80 MHz and the bandwidth of the 5 GHz band is about 570 MHz. Therefore Wi-Fi can transmit data faster on the 5 GHz band because it is wider.
*The ranges given here aren't 100% accurate. The way the FCC splits up the electromagnetic spectrum is complicated.
Interference
Microwaves are a huge source of interference for Wi-Fi. Microwaves heat up food by showering it with 2.4 GHz radiation. Some of this radiation leaks out and confuses Wi-Fi receivers when the microwave is running. Cordless phones also often operate on the 2.4 GHz band. The 5 GHz band is used by fewer devices, so the amount of interference on it is less.
Range
The radio engineer formula gives the path loss in db:
L=20*log10(4*pi*d*f/c)
where L is the path loss in decibels, d is the distance traveled by the signal, f is the frequency of the signal, and c is the speed of light. Based on this equation, we can expect the path loss to be 20*log10(5/2.4) = 6.3752 dB more for a 5.0 GHZ signal than a 2.4 GHz.
Transmit a pair of signals at 2.4 GHz and 5.0 GHz with 100 mW of transmit power each. If the 2.4 GHz signal received is 10 mW, then the 5 GHz signal will only be 2.304 mW at the same receiver.
Photo by Bill Smith