Shaykh, a question: regarding witr, is it allowed for her to pray witr five minutes before the adhan of fajr?

Yes, regarding witr, the Prophet ﷺ said as narrated in the hadith of Abdullah ibn Umar: The night prayer is two by two, and if one of you fears that dawn is near, let him pray witr with one rak'ah.

And "fears" here means that dawn is approaching. The Prophet ﷺ preferred praying at the end of the night, and he said: Make the last of your night prayers witr.

Also, the Prophet ﷺ approved of Umar delaying his witr.

Until the end of the night, and his qiyam would be at the beginning of the night, as in the hadith of Sa'd ibn al-Musayyib, that the Prophet ﷺ asked Abu Bakr, may Allah be pleased with him, about his night prayer, and he said: I pray witr before I sleep.

The Prophet ﷺ said: He is careful. Then he asked Umar ibn al-Khattab about his witr, and he said: I pray witr at the end of the night and sleep at its beginning.

The Prophet ﷺ said to Umar: This one is strong, or this one is firm. So we say that what concerns prayer at the end of the night, the Prophet ﷺ prayed it, and his sahaba prayed it.

And the Messenger of Allah ﷺ guided to it, in fact, it is the best thing to do.

In that, performing witr at the end of the night, except if a person thinks he will not get up, then he should pray witr before sleeping, whenever he sleeps. And Allah knows best. May Allah reward you with goodness.