[OP has clarified the somewhat unorthodox behaviour of the calculator; my earlier answer, preserved below, no longer applies but we can do something else instead.]
Do this:
+ 4 + 7 sq - 4 4 =
That will
add 4+7 to our initial 5, getting 16; square it, getting 256; subtract 44, getting 212.
We have used
9 keypresses in total.
If we need to use the full 12 keypresses, we can
follow up with + 0 = which of course changes nothing.
Old answer, applicable to real calculators
I think I can do it in 11 key presses:
sq - 4 - 7 = sq + 4 sq =
So
after squaring the calculator shows 25; we subtract 4 and 7 to get 14; we square to get 196; we add 4^2=16 to get 212.
If we need to use exactly 12 key presses we can
press = after subtracting 4.