iMac 10.5.8 Target Display Mode Question

I have a 20" mid 2007 iMac version 10.5.8. I'm looking to use this as a second monitor for my Macbook Pro (15" early 2013 version 10.10.4). I'm wondering whether I can update the iMac's operating system to version 10.6.1 and use target display mode. According to Apple's description of target display mode (https://support.apple.com/en-us/HT204592), there are three requirements to use target display mode: (1) A Mac notebook or desktop with a Mini DisplayPort or Thunderbolt port, (2) A Thunderbolt cable or a Mini DisplayPort to Mini DisplayPort cable, and (3) A supported iMac with OS X v10.6.1 or later. My iMac has a mini display port and I can easily buy the appropriate cable/converter online. I'm just not sure whether upgrading the OS X to version 10.6.1 will work or not. Particularly because the earlier link also lists the iMac models that support target display mode and the earliest model is a late 2009 iMac.

I've tried a few alternatives like ScreenRecycler and AirDisplay, but both lag quite a bit which makes having the extra screen pretty useless/annoying to work with.

Any feedback/suggestions would be great! Thanks!