Add the whole numbers and fractions separately with the same denominator.<br><br>
&bull; \( 4\frac{23}{48} + 1\frac{23}{48} = (4 + 1) + \left(\frac{23}{48} + \frac{23}{48}\right) \)<br>
&bull; Whole numbers: 4 + 1 = 5<br>
&bull; Fractions: \( \frac{23}{48} + \frac{23}{48} = \frac{46}{48} \)<br>
&bull; Simplify \( \frac{46}{48} \): divide numerator and denominator by 2.<br>
&bull; \( \frac{46}{48} = \frac{23}{24} \)<br>
&bull; Answer: \( 5\frac{23}{24} \)<br><br>
Final Answer: C: \( 5\frac{23}{24} \)