This is not correct.

In shafi fiqh i was told that one cannot pray his sunnahs salah until he’s made up for his missed faraid.

Prayer | March 25, 2014 4:40 am
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During the shad ah in tahahhud I recited it in tajweed. Meaning I did it incorrectly because I didn’t pronounce the noon correctly. Do I have to repeat those prayers.
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I am a young new Muslim studying. Where I am living is quiet far from the masjid. I am finding to attend all five prayers and spend time with my wife and study very strenuous. If I intend to make all five it would leave me with about one to two hoursat home barely any time to eat etc. With going fajr and isha prayers it leaves me usually 5 or less hours sleep and taking its toll on me. There is a closer sufi mosque but they pray isha earlier then the time comes in but I don’t always feel comfortable praying there. What would you suggest I sometimes pray maghrib at home but it doesn’t keep emaan as high. Also I don’t have much time to teach my wife.