Add the whole numbers and fractions separately with the same denominator.<br><br>
&bull; \( 4\frac{7}{16} + 1\frac{7}{16} = (4 + 1) + \left(\frac{7}{16} + \frac{7}{16}\right) \)<br>
&bull; Whole numbers: 4 + 1 = 5<br>
&bull; Fractions: \( \frac{7}{16} + \frac{7}{16} = \frac{14}{16} \)<br>
&bull; Simplify \( \frac{14}{16} \): divide numerator and denominator by 2.<br>
&bull; \( \frac{14}{16} = \frac{7}{8} \)<br>
&bull; Answer: \( 5\frac{7}{8} \)<br><br>
Final Answer: C: \( 5\frac{7}{8} \)