Are Cat5e fully compatible with GBabit specification? What the main difference between Cat6?
Would like a proof if possible.
The main different between each version of the Cat specification is the numbers of twists per length of the cable.
Two wires running in parallel will create cross-talk. That is, if a current is running down one of the wires, the parallel wire will generate a current as well directly proportional to the distance between the wires and the current running in the wire. This is how a transformer works.
Twisting the wires interrupts this cross-talk, resulting in a cleaner signal as current running in one wire producese less of a current in the other wires. As signal speeds increase, the importance of cross-talk-free wires becomes more and more important and thus the twisting requirements become more and more stringent.
Cat6 has more dense twisting of the wires so that it produces a cleaner signal on each individual wire and thus will produce fewer errors allowing for higher communication speeds than Cat5e, Cat5, or any lower numbered Cat specification.
Technically, Cat5 can support Gigabit communication, but the primary factors would be the length of the cable involved and the environment the cable is running through. You may only get a Gigabit signal over a few feet of Cat5 or Cat5e while using Cat6 would allow you to send a solid and reliable Gigabit connection over dozens of feet without issue.
UPDATE for OP additional question: You are always playing odds with any situation like this. If you have low quality Cat5e, and/or low quality networking components, and/or your network cords run parallel to power conduit or telephone you'll find you have much, much less than 100m before you'll have difficulty running Gigabit over Cat5e.
Using Cat6, which was desiged for Gigabit, is much less likely to experience significant signal degredation when faced with similar problems.
Because there are so many factors you must take into account, there is simply no way for us to tell you "Cat5e will always allow stable and fast Gigabit connections if the run is less than x feet". And so we play odds. And so I will state that the odds are that, if you're dealing with lines parallelling power conduit or phone, if you're dealing with runs longer than several feet, and if you're dealing with consumer-grade components that will be connecting over these lines, you will not experience a speedy and stable Gigabit connection between all your components. It's possible you will have a perfectly OK connection. I just think there is a signficant likelihood that you won't unless you use Cat6.
However, since you've already run the cable, there's really no sense in tearing it all out unless after you've tested the lines and found whether or not their performance meets your needs.