If the load current and flux of a DC motor are held constant and the voltage applied across its armature is increased by 5%, the speed of the motor will increase by 5%.

The speed of a DC motor is directly proportional to the voltage applied to its armature. According to the motor speed equation:

N = (V - E) / kφ

where N is the speed, V is the applied voltage, E is the back electromotive force (EMF) of the motor, k is a constant, and φ is the flux.

If the load current and flux are held constant, and the voltage applied to the armature is increased by 5%, the numerator of the equation (V - E) will increase by 5%. Since the denominator and the other variables in the equation remain constant, the speed N will also increase by 5%.

Therefore, the correct answer is B: Increase by 5%. The speed of the DC motor will increase by 5% when the voltage applied to its armature is increased by 5%, with the load current and flux held constant.