I've just purchased a used Mac Pro that was sold to me as a "5,1" model, which according to everymac.com and Apple's support site, should be a Mid 2010 Mac Pro. However the model display in System Information/About this Mac shows it as an "Early 2009", as does the Apple warranty check.
It does have the 3.2GHz Quad Core Xeon processor which was only available with the Mid 2010 model (again, according to everymac.com) and the latest firmware for the 5,1 Mac Pro. I'm not sure if the latter is an indicator though as some searches around the web suggest that it was possible to upgrade an Early 2009 model with the 5,1 firmware which should make it a Mid 2010.
So, I'm wondering if this is just a case of Mid 2010s reporting themselves as Early 2009 Mac Pros in general, or if this model has had both an upgraded firmware and upgrade processor?
I think the model name shown in System Information is determined from information encoded within the serial number. It looks like the precise details of this are private to Apple, but some information is given in this MacRumors post (which includes the image below), and it looks like some sites may have reverse engineered it.
Be aware it is possible under some circumstances to change the serial number reported to the software running on the machine. Specifically: logic boards supplied by Apple to service providers have a "blank" serial number, and service providers must "serialize" them (this is only possible once, from the service provider point of view) by running some special software and providing the desired serial number via keyboard input. (This is why I suggested checking the serial number printed on the hardware in my comment on the question.)