Is it permissible to delay the prayer for someone who woke up two minutes before its time expires, and it is highly probable that the time will expire if he performs ablution (wudu) or a full ritual bath (ghusl), taking into consideration other matters such as obeying one's mother or searching for water?

Whoever wakes up a short time before the prayer time expires must immediately perform purification and prayer according to the majority of scholars. According to the Malikis, one should perform tayammum and pray if there is not enough time for ghusl or wudu. As for the Shafi'is, they differentiate between two cases: If the remaining time is only enough for purification or a part of it, then immediate qada' (making up the prayer) is not obligatory. However, if there is enough time for purification and a part of the prayer (even if only the takbirat al-ihram), then performing it immediately is obligatory, and delay is not permissible. If one delays until the time expires, they are sinful, and immediate qada' becomes obligatory. The most correct opinion is that of the majority, which states the obligation of immediately performing purification and prayer.