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

Yes. Because of daylight saving time the gap moves between −1h and 0.

When is the best time to call Nairobi from Cairo?

Between 09:00 and 17:00 in Cairo, which is 09:00 to 17:00 in Nairobi.

Cairo and Nairobi are on the same local time. This gap is not fixed: daylight saving time moves it between −1h and 0 during the year.

Cairo

Egypt

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Nairobi

Kenya

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A 9-to-5 day in each city overlaps for 8h. That is 09:00–17:00 in Cairo, which is 09:00–17:00 in Nairobi.

City	Time zone	UTC offset
Cairo · Egypt	Africa/Cairo	UTC+3
Nairobi · Kenya	Africa/Nairobi	UTC+3

What is the time difference between Cairo and Nairobi?: Cairo and Nairobi are on the same local time. This gap is not fixed: daylight saving time moves it between −1h and 0 during the year.
Does the time difference between Cairo and Nairobi change during the year?: Yes. Because of daylight saving time the gap moves between −1h and 0.
When is the best time to call Nairobi from Cairo?: Between 09:00 and 17:00 in Cairo, which is 09:00 to 17:00 in Nairobi.