yes you can have internet on both laptops.
here are the general steps in sharing your internet connection in two or more pcs..
•go to your router setup (which is usually 192.168.1.1 or 192.168.2.1 you should know what is the IP of your router)
•you will be prompted to enter username and password
if you haven't been to this router setup, just enter the default username and password
(it is provided in the router's manual)
•in the router setup, look for WAN setup or WAN port or similar
•enter or choose a port type as "POPoe" then enter your ISP username and password in the fields if there will be a connection type input then choose "continuous" otherwise continue to next step.
•look for LAN settings, there is an option to enable DHCP server, enable it! if there will be inputs on
IP - then enter your routers address
IP Subnet Mask - usually it is 255.255.255.0
if there is an IP Address Pool just leave it.
•save all your settings usually it is by "apply and reboot you router" or something alike. or if there is a separate save settings on every "settings" save it before you continue to another setup. example: if you already configured your WAN settings then there is a save button then hit it b4 going into LAN settings..
•reboot you router
•wait until connect
•check the internet status the router setting if you are connected
•just keep you two laptops detects automatic internet connections, don't give them a static LAN Ip address unless you know what you are doing.
•then your done!
note:
connect the CAT5 into the switch uplink then connect the computers the the switch's downlinks