Two ropes, AD and BD, are tied to a peg on the ground at point D. The other ends of the ropes are tied to points A and B on a flagpole, as shown below:

Two ropes, AD and BD, are tied to a peg on the ground at point D. The other ends of the ropes are tied to points A and B on a flagpole. Angle ADC measures 45 degrees, and angle BDC measures 30 degrees. The length of DC is 5 multiplied by square root of 3.

Angle ADC measures 45°, and angle BDC measures 30°. What is the distance between the points A and B on the flagpole?