5 hours and 36 minutes =  hours =  hours =  hours.

Now, the effective velocity of the plane with the wind is  = 560 miles per hour (I divided the distance by time to get the speed).


It is the sum of the plane speed at no wind "u" and the speed of wind "v".

It gives you your first equation 

u + v = 560.



Next, the effective velocity of the plane flying against the wind is  = 500 miles per hour (I divided the distance by time to get the speed).


It is the difference of the plane speed at no wind "u" and the speed of the wind "v".

It gives you your second equation 

u - v = 500.


Write these two equations together

u + v = 560,    (1)
u - v = 500.    (2)


Now ADD the two equations (both sides).  You will get

2u = 560 + 500 = 1060.   Hence, u = 530 miles per hour.


Thus you just found the speed of the plane at no wind. It is 530 miles per hour.

Now from equation (1) v = 560 - 530 = 30.


So, 30 miles per hour is the speed of the wind.


Answer.  The speed of the plane at no wind is 530 miles per hour.
         The speed of wind is 30 miles per hour.