I also have a Nuvi 5000. Here's how to get the map onto your computer.... but you aren't going to like this

1. Buy the City Navigator DVD
2. Load it onto your computer
Unfortunately, the map stored on the Nuvi (this applies to all of the Nuvi line) cannot be copied to the computer in the correct form to use in mapsource. If this is important to you, call (do not e-mail) Garmin support and tell them what you want to do, and that you are surprised and disappointed you can't just copy the map to your computer.
People report varying results from this, depending on how nice you are and the luck of the draw. They may offer to send you the DVD for $15 to cover shipping/handling. Some people have actually gotten it for free. Others have gotten nowhere and had to buy at full retail.
One other possibility. If you just got this unit, you may be eligible for a free map update when you register it at garmin.com. If so, be sure that Mapsource is installed on your computer first. Then download the free update. When you finish the process, the City Navigator maps will be automatically installed in Mapsource. I did this myself and was pleasantly surprised because I didn't expect it.