I am assuming you work from home? or have an office connected directly to your personal living space?
Otherwise I can't see how you would have both of these wired connections at a work place.
The easiest way would be to put a wireless router on your home ethernet and plug in your (wired) work ethernet.
Or.... if you have to keep both wired for some reason, put another short Cat5 and a connector on it. So you aren't plugging/unplugging from your computer and instead are plugging/unplugging from the connector.