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5 2/3 is 17/3, so the reciprocal is 3/17. 

When a problem asks you for a reciprocal, you just flip the numerator and the denominator.
A reciprocal of a fraction is acquired by interchanging the numerator and the denominator or just inverting the fraction. In the given fraction above, 5 2/3 is equivalent to 17/3. To invert this, or to interchange the numerator and the denominator, the reciprocal of this fraction, therefore, is 3/17. The correct answer is 3/17.