two and a half diggers

or, in the context of the task, the habrouser

I published here a habrotopic and at some point in time I received a rating of 5. With a number of votes at 12 :)
The subconscious mind formed by the mathematical-technical education began to rebel. I asked him what was the matter.
In general, if anyone finds a solution to the following system in integers, there is some kind of bonus :)
x + y = 12
xy = 5

It is clear that this is due to the fact that not all data is displayed on the page at one time. What will web programming connoisseurs say?

UPD: Well, here again :)
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