I live in a small city with no mosques in it, it is 1.30 hours drive from Chicago, IL . I know there are 5 methods to calculate prayer times
Muslim World League
Egyptian General Organization
University of Islamic Sciences
Islamic society of North America
What are the differences between them, as each one gives me different prayer times. Which one should I follow? I have no mosque in here to follow its Azan thou. Does it have something to do with the Madhabs?
All these calculation methods have some error ratio and the value of this ratio increases if you use the wrong method for the wrong location, as each method works best with a specific location. Which means in your location the ISNA (Islamic society of North America) method will be -at least among- the best.
Most of these methods consider special rulings of different madhhabs, so one can't pretend the time differences have to do with madhhab view rather than with errors in the calculation methods which rely on more or less localized data.
For example the Umm al-Qura method works best in the Arabic peninsula in other places this method may give you prayer beginning times that are either too early (which is definitely bad) or too late (which might be good if you don't wait till the end time of a prayer to pray).
In Europe (at least south and middle Europe) the Muslim world league method is fine.
More or less has to do with Madhab, Fataws and opinions of the Quran and Sunnah. Feel free to use anytime you want, whichever suits you best. For example, I usually pray Jumma an hour before or after Asr prayer based on which Masjid I go to (depending on my needs).
Here are some good source on the calculations, how they are done and why (too large to be adding them to this post):
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