ArcGIS for Enterprise 10.5.1
good guess would be before user conference
These types of questions typically don't get answers from Esri staff. If they do get a response, it is usually fairly general and not as or more specific than month.
Looking at the ArcGIS for Desktop Product Life Cycle Support Status document gives some insight:
There has been a bit of slippage each year with the spring releases. Looking at the trend above, I would guess sometime mid-June. That said, I think Dan's answer is the most certain, i.e., before UC.
Maybe you'd like to revise those years? (10.2.2 - 2014; 10.3.1 - 2015)
Based on the current schedule as I know it, Dan has the right idea.
Thanks Joshua & Dan, that is very helpful.
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