Ios7 on iPhone 4 won't connect to iTunes?

Whenever I try to connect my iPhone to itunes, itunes tells me that I have an incompatible version of itunes. It tells me to go to itunes.com and download the most up to date version; however, the most up to date version of iTunes requires that I have Mac OSX 10.6.8 or later. I only have OSX 10.5.8.Is there any way around this? (Besides getting a newer computer)

No, there's no way around this. You will have to get a newer Mac just to get iTunes support again.