Is it permitted to pray in state of Janabah, if time will run out in doing ghusl?

I want to ask, If a person wakes up at home from his regular night sleep in a state of Janabah and his condition (after he wakes up) is that: 1) he is not deprived of water at his home. 2) he has not yet taken a bath (in a state of Janabah) 3) He is also has not done the Fajr prayer (Subuh). 4) He wakes up at 5 minutes (or less) before sunrise. What should he do in this case, should he take a bath first and risk missing / skipping the Subuh prayer by bypassing its time limit (sunrise)? (because taking a bath in a state of Janabah will surely take longer than normal bath, presumably more that 10 minutes) Or should he just take a regular wudu right after he wakes up and attempt to do the Subuh prayer without taking a bath (praying in a state of Janabah)? Thus making it possible for him to start the Subuh prayer within its time limit. Which one? Regards