Cat 5 was supposed to run at 100 Mbps, but there were problems with it so they made some improvements and came out with Cat 5e and it improved it so well it can go all the way up to 1 Gbps now. Cat 6 is the newest version and was originally designed to go up to 1 Gbps but can now run up to 10 Gbps.

Category 6
The need for this increased cabling bandwidth is the ongoing development of higher speed protocols. Category 5 cabling, when launched a decade ago had a much higher capability than the 10M Ethernet or 16M token ring protocols used but it has now reached the end of its lifetime with the advent of Gigabit Ethernet. Category 6 now provides additional headroom and as a result, new developments in higher speed protocols will concentrate on Category 6 performance. Category 6 increases lifetime capabilities, ultimately resulting in a maximum return on investment.
The general difference between Category 5e and Category 6 is in the transmission performance, and extension of the available bandwidth from 100 MHz for category 5e to 200 MHz for category 6. This includes better insertion loss, near end crosstalk (NEXT), return loss, and equal level far end crosstalk (ELFEXT). These improvements provide a higher signal-to-noise ratio, allowing higher reliability for current applications and higher data rates for future applications.
Because of its improved transmission performance and superior immunity from external noise, systems operating over category 6 cabling will have fewer errors vs. category 5e for current applications. This means fewer re-transmissions of lost or corrupted data packets under certain conditions, which translates into higher reliability for category 6 networks compared to category 5e networks.