Does the time difference between Beijing and Cairo change during the year?

Yes. Because of daylight saving time the gap moves between +5h and +6h.

When is the best time to call Cairo from Beijing?

Between 14:00 and 17:00 in Beijing, which is 09:00 to 12:00 in Cairo.

Beijing is 5h ahead of Cairo. This gap is not fixed: daylight saving time moves it between +5h and +6h during the year.

Beijing

China

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Cairo

Egypt

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A 9-to-5 day in each city overlaps for 3h. That is 14:00–17:00 in Beijing, which is 09:00–12:00 in Cairo.

City	Time zone	UTC offset
Beijing · China	Asia/Shanghai	UTC+8
Cairo · Egypt	Africa/Cairo	UTC+3

What is the time difference between Beijing and Cairo?: Beijing is 5h ahead of Cairo. This gap is not fixed: daylight saving time moves it between +5h and +6h during the year.
Does the time difference between Beijing and Cairo change during the year?: Yes. Because of daylight saving time the gap moves between +5h and +6h.
When is the best time to call Cairo from Beijing?: Between 14:00 and 17:00 in Beijing, which is 09:00 to 12:00 in Cairo.