A fifth has an inverse relationship with the interval of a fourth, which is made up of five half-steps. If you stack the two on top of each other, you would get an octave. Going up from a root note by a fifth results in the same note name as going down by a fourth, and vice versa. Consequently, the two intervals are easily confused.
If you play two notes a fifth apart from each other at the same time, they blend together quite a bit (if the notes are in tune). In music theory, this is called "consonance," and a fifth is one of the most consonant intervals, second only to an octave. This is why it is often called a "perfect fifth."
To be more precise, the sound waves of two notes a fifth apart from each other have almost exactly a three-to-two relationship. For every two vibrations of the lower note, there are three for the higher note (in reality there's a tiny discrepancy, but it's close enough that the ear can't tell the difference).