Not sure about five, but you can make 42 with 6 2s with this method:
2[(22)! - (2/2) - 2] = 42
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22 + 22 - 2 = 42
You can use three 2s to make 26 as follows (2x2)! + 2 = 26 So you can simply make 26 with five 2s as (2x2!) + 2 - 2 + 2 = 26
(2x2x2)/2 + 2
Two will go into forty two twenty one times.
(22/2+2)x2