3 years is reasonable safe, but it isn't guaranteed.
The 5,1 model isn't "new" relative to extended support lifecycle. It is only already on the countdown to vintage/obsolete status. Apple's policy for hardware is pretty straightforward.
legacy and obsolete: 5-7 years after stop selling them, the hardware support dies off.
https://support.apple.com/en-us/HT201624
Apple's policy for software for obsolete hardware is less explicit but pretty standard. They won't past the obsolete/vintage status. Drawing a support distinction between obsolete hardware and obsolete software is way off standard practices. They run as a coupled system, if a major part of the system is obsolete any attempt to swim upstream of that for just one half is relatively high cost which vendors typically don't do (especially for free; not sky high service contract). Apple could cut things off early. They aren't going to create a "add this mix of aftermarket 3rd party modifications and then" certification matrix for the 5,1. When the standard 5,1 config hardware goes out of OS X coverage scope the 5,1 will also.
Clock is ticking on the 5,1. It has been a bit slower than most Mac products because of the large gulf between 5,1 introduction and stopped selling them (Oct 2013). It is already at the +2 years mark. 5 years to vintage means only have 3 years left on hardware (and a highly likely hard deadline on software). That large gulf may not be a positive winner for software though. The GPUs of the 2010 model are at the 5 year mark now. The 2012 speed bump to the 5,1 didn't add any extension in that respect. In 3 years those will be 8 year old GPUs. That year 3 operation has a pretty significant risk factor on it. There is some reasonable likelihood the then current OS X will be in a "happens to work" zone (perhaps with some hacks) , not an Apple supported one for the then current OS X. However, Apple's OpenGL progress is glacially slow and the GPUs of the current low end Mac GPUs don't leave the 5770 in the dust behind them on performance. Those are factors toward OS X coverage continuing. ( keeps it out of the "drop as soon as possible" category.)
If your standard practice is to sit 2 years back from current on OS X releases then 3 years is a pretty solid outcome. Another two years of OS X upgrades that cover the 5,1 has a very good chance of happening.
P.S. vintage is a 5-7 year window. However, given the 5,1 is a 2010 design that was stretched into 2013 .... it is extremely likely only getting the low end of that range. That 2 year "slack time" got burned up in the 3 year delay. If anything Apple is going to be looking for any early exit they can take, since they more than burned through that slack time.
