Determine the remaining sides and angles of the triangle $A B C$.
\[
A=110^{\circ} 40^{\prime}, C=50^{\circ} 20^{\prime}, A B=5
\]
\[
B=
\]

Step 1 ：Given two angles and one side of a triangle, we can use the law of sines to find the remaining sides and angles. The law of sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is the same for all three sides and angles.

Step 2 ：First, we can find the remaining angle B by subtracting the given angles A and C from 180 degrees, since the sum of all angles in a triangle is 180 degrees.

Step 3 ：Then, we can use the law of sines to find the remaining sides.

Step 4 ：Given: \(A = 110.67^\circ\), \(C = 50.33^\circ\), \(AB = 5\)

Step 5 ：Calculate: \(B = 180 - A - C = 19^\circ\)

Step 6 ：Using the law of sines, calculate: \(BC = \frac{AB \cdot \sin(C)}{\sin(A)} = 4.11\)

Step 7 ：Using the law of sines, calculate: \(AC = \frac{AB \cdot \sin(B)}{\sin(A)} = 1.74\)

Step 8 ：\(\boxed{\text{Final Answer: The remaining angle and sides of the triangle } ABC \text{ are: } B = 19^\circ, BC = 4.11, AC = 1.74}\)