Is it permissible for a Muslim to pray the obligatory prayer a short while (five or ten minutes) before its time, due to an excuse such as travel or the start of a class, knowing that the most beloved deeds to Allah are prayers performed on time?

Prayer is not valid before its due time, whether based on certainty or strong probability. This applies to both residents and travelers. However, while traveling, it is permissible to combine the Asr prayer with the Dhuhr prayer, and the Isha prayer with the Maghrib prayer, by performing them earlier (jama' taqdim). It is not permissible to combine the Maghrib prayer with the Asr prayer. If a traveler intends to stay in a country for more than four days, he is no longer considered a traveler and is not permitted the concessions of travel, such as combining and shortening prayers.