Cat 5 cable versus Cat 6 cable

Does anyone know if there is a difference between RJ45 connectors and Cat 5 cable versus Cat 6 cable. The cat 6 (1 gigabite) cable I have is thicker than my Cat 5 cable. The wires do not push in as easily into the CAt 5 RJ45 connector as they do with the CAt 5 cable. This makes it difficult to get a connector crimped correctly. I bought my RJ45 connectors at Home Depot. Any suggestions would be appreciated