Selection C is appropriate.
Divide by 4, unfold, subtract 1/3.
.. |x +1/3| = 5
.. -5 = x +1/3 . . . . one choice for the sign of the content of |x +1/3|
.. -5 1/3 = x
.. x +1/3 = 5 . . . . the other choice
.. x = 4 2/3
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If this were an inequality |x +1/3| < 5, I would "unfold" it as
.. -5 < x +1/3 < 5 . . . . . . . copy the right side expression to the left with reversed sign.
The above is an approximation of that. You can't really write -5 = ( ) = 5, because it is a gross violation of the equal sign. But you can write the two versions:
.. -5 = ( )
.. ( ) = 5