Does iTunes 10.5.0.142 not support the original iPhone? I have the original iPhone and I cannot seem to get it recognized by iTunes 10.5.0.142. I followed the troubleshooting advice at http://www.apple.com/support/iphone/assistant/itunes/, but it did not seem to help. Is it no longer supported by iTunes?
iTunes does support the original iPhone, there is no where it is written in the requirements of iTunes 10.5 that says that iTunes requires this version of iOS or this particular iPhone or even iPod in order to sync with it. All Apple music devices should be supported unless other wise noted.

The only point where it may matter is if you have updated to the latest version of iOS from a newer version of iTunes (e.g. greater than 10.5.0.142) and then are attempting to use that updated iOS on an older version of iTunes 10.5.0.142 in this case. 

In that situation there may be issues communicating between the two due to apple changing protocols or who knows what else between versions of iTunes and iOS. I suggesting updating to the latest version of iTunes, and then contact Apple or their discussion forms if the problem persists.