You want eth0:1
as 192.168.1.5. Don't change the default gateway. Note the ":1" after eth0. That is the notation for a virtual interface.
sudo /sbin/ifconfig eth0:1 192.168.1.5 netmask 255.255.255.0
If you then enter in "/sbin/route", you should see that there is a route for the 192.168.1.0 network on eth0:1.
This is if the 192.168.1.2 computer is on the same network segment. In other words, if both computers are plugged into the same switch.
If the windows machine bridges two networks, and the windows machine isn't the default gateway, then you would simply add a route. You wouldn't create a virtual device because you need to be on the same network as the windows gateway interface:
route add -net 192.168.1.0/24 gw 18.104.22.168 dev eth0
There is a Network Administrator's Guide (nag.pdf) book on the www.tldp.org
website. I highly recommend it.