Two more things came to mind:
1) Typically, you want to use a crossover cable between switches ... especially ones that don't employ uplink ports. I suggest re-reading the manufacturer's documentation that came with your switch to see if their switch was designed to not require MDI/MDI-X crossover cables. I'm pretty sure the Linksys EG008W supports this ... so this shouldn't be an issue.
2) If you want Gigabit bandwidth, regardless of which cable (CAT5, 5e, or 6) that you use, all four pairs (8 connectors) will be required. Some homes, with pre-built in CAT5, also employ running both LAN & Telephony, over CAT5, by installing dual-use outlet plates. If yours is wired this way it would be considered non-standard ... and Gigabit Ethernet will NOT work. In fact, you could cause equipment damage with this arrangement if you try to deploy Gigabit as Telephony runs power (up to 150 volts) over one of these pairs.