Cat 5 and Cat 6 are quite similar however there are a few differences.
Cat 5 is desgined for 100 Mhz operation. 10/100 speed mainly. Some good quality cat 5 will allow gigabit ethernet throughput.
Cat 6 is desinged for 250Mhz and is better for running a goog gigabit network. Cat 6a is desinged for 500Mhz and can be capable of 10Gb networking.
I use cat 5 for my gigabit home network, but to be honest, i do find some significant differences in performance between cableing.
Ther also can be a difference in cable thickness as cat 6 tends to have better shielding to provide the better performance.