I recently bought a Toshiba X500 laptop with decent speakers & sound card in it. I want to use headphones but im unsure if they also need to have the same audio channels as the sound card (5.1 in this case). Also The laptop itself only has the two standard sound ports - headphones and microphone, does 5.1 headphones require a special kind of connection?.
5.1 means "five loudspeakers and one subwoofer". As such, you can only use 5.1 sound if you actually connect five loudspeakers and one subwoofer. If you use those five loudspeakers and one subwoofer and position them according to the manual around your listening position, you will be able to hear sounds from all around you ("surround sound").
However, any 5.1 capable soundcard is also able to support any lesser configuration, i.e. Stereo/"2.0". The quality of sound is not affected by that, but of course two loudspeakers/headphones will not be able to produce sound that "comes from behind".
To answer your question: Yes, you can just use your normal headphones or laptop speakers. However, they will work in stereo configuration and will not produce surround sound.
(One exception: There is at least one sound card (Creative X-Fi) that is able to simulate surround sound using stereo headphones and some fancy signal processing.)
You can use regular stereo headphones with your 5.1 sound card, you will however, only get 2 channels of sound. If you are looking to get some 5.1 headphones, they will not use the same 3/4 in headphone jack your microphone and regular headphones use. They will likely use something like USB.