How can a Muslim make up for missed prayers spanning five months?

Abandoning prayer is a grave sin, one of the greatest major sins. The prophetic traditions (hadiths) explicitly state that one who abandons it is a disbeliever, as the Messenger of Allah, peace and blessings be upon him, said: "Between a man and polytheism (shirk (definition)) and disbelief (kufr) is the abandonment of prayer." It is obligatory for the servant to hasten to make up for the prayers he missed immediately, according to his ability, whether by night or day, while observing the correct order among the missed prayers.