It's well researched, the traits were not 'designed', rather the traits popped out of linguistic analysis and statistics, and it's stable across different populations and over most of a person's lifetime.
There is an open test called the IPIP Neo which has either 120 or 300 questions, which you can take online [2].
If you're really interested in what is being taught these days about the theory, this is a good set of lectures take takes you from the early theory of personality through to what is considered science today [3].
[1] http://en.wikipedia.org/wiki/Big_Five_personality_traits
[2] http://www.personal.psu.edu/~j5j/IPIP/
[3] https://www.youtube.com/playlist?list=PL22J3VaeABQAhrMCQUa6s...