Yes if when you put the new I5 in the cpu slot it posted the board for a second and shut down.
It likely needs a bios firmware update on the motherboard so it can support your new I5 cpu.
The board being from a Gateway pre built system though may be a problem.
You should find any bios firmware update files from the Gateway support section of there webpage on the internet.
But don`t be surprised if there is no new bios firmware revision for your motherboard over the version you currently have running on the Mobo. Gateway and a like can sometimes be a bit behind with bios updates for there pre built pc systems.
If you don`t have the link to support click bellow.
http://us.gateway.com/gw/en/US/content/drivers-downloads