No, the impedance of an antenna will never be 50 Ohms (a nice generalization), there are a number of parameters to consider in designing an antenna, and you always sacrifice a number of them to get somewhere near a specified target, and impedance is definitely one of them. In reality it is rarely of great importance on low power transmitters or receivers, which is all that you are allowed to use in this band, it's all about acceptable VSWR against bandwidth, directivity etc.For a start, you say you wish to build an antenna for 5.8GHz. What sort of antenna, and how do you plan to measure it's performance. There are dozens of potential antenna types for 5.8GHz, and in reality, if you want a fully characterized antenna, then you either buy one or have appropriate test gear, which doesn't come cheap. (If you drop down to 2.4GHz, then there are some cheap network analysers available )There is finite analysis software which allows antenna designs to be computed, but don't expect this to be easy to learnPerhaps the simplest to build is a wire whip antenna, 1/4 wave are often used to keep them as compact as possible. There is a lot of information on the internet on how do design for 2.4GHZ, which will apply at 5.8GHz. You can tweak these antenna by bending the arm with respect to the ground plane to get close to 50 Ohms, but in doing so you trade off other performance characteristics. Why bother?Cheers,Richard