I don't see that you need radians for this problem. The angular information you have (in part a) is in degrees. The answer you seek (in part b) is also in degrees. So, you might as well do the problem in degrees.
You know the radius of the pulley, so you can calculate the circumference. You know once around the circumference is 360 degrees. What fraction of 360 degrees is 78° 40' ? Use that same fraction with the circumference to find out how much the weight will be raised.
For part b, find out what part of the circumference is 5 inches. Use that same fraction with 360 degrees to find out how much the wheel should be rotated.
My policy is to not respond to homework questions with an answer that you can copy. You are given homework to help you figure out how to solve problems. You may face a similar problem in the future, but the numbers will be different. You can't always go to the Internet for help.
In addition, some teachers give homework to help find where student's weaknesses are. If a student has trouble with a homework question, it is better that the student get help from the teacher than from the Internet.