Multiple screens on mid-2007 iMac with Mavericks os

Hello Peartree327,
I understand that you are trying to get your iMac to have a TV as it's secondary display. Let's go over what you can do to get that working.
That port for video on the right is going to be a Mini-DVI port. You would pair that plus a DVI to HDMI cable, you should be able to get video to your TV. Take a look at the articles below to go over the tech specs and information about the adapters to get you sorted out.
iMac (Mid 2007) - Technical Specifications
https://support.apple.com/kb/sp16
About Apple video adapters and cables
https://support.apple.com/en-us/HT201853​

Apple Mini-DVI to DVI Adapter

Part: M9321G

Compatible with:

• MacBook (13-inch, Mid 2009)
• MacBook (13-inch, Early 2009)
• MacBook (13-inch, Late 2008)
• MacBook (13-inch, Early 2008)
• MacBook (13-inch, Late 2007)
• MacBook (13-inch, Mid 2007)
• MacBook (13-inch, Late 2006)
• MacBook (13-inch)
• Mac mini (Late 2009)
• Mac mini (Early 2009)
• iMac (Early 2008)
• iMac (Mid 2007)
• iMac (Late 2006)
• iMac (Early 2006)

Belkin HDMI to DVI-D Cable (2 m/6.6 ft.)
http://www.apple.com/shop/product/HHM62ZM/A/belkin-hdmi-to-dvi-d-cable-2-m-66-ft
Take care.

2007 iMacs have Mini DVI ports, if you want to connect an external display you need a Mini DVI to HDMI or VGA or DVI adapter depending on the connections the external display has. If you choose HDMI this will NOT transmit audio, in 2007 that ability was not possible to go from Mini DVI (strictly video) to HDMI.

That is a mini-DVI connector.

Your welcome.