[Ali Imran]

I know that profession of faith and practice of faith have often been taught in Islam. My understanding is that the way to gain salvation includes reciting the creed, praying 5 times a day toward Mecca, fasting one month a year, giving one-fortieth of their income, and make the pilgrimage once in their lifetime to Mecca. Muslims who faithfully practice these go to heaven, and those who do not will go to hell. Working out their salvation is seen as working for their salvation. All seems well and good except for the fact that they've not been "born again."

That is false. 

Our salvation depends on the mercy of Allah. We obey Allah's commandments and do good deeds which Allah loves, all in the hope that Allah will have mercy on us.

Allah may be merciful to somebody who never prays 5 times a day or fasts in Ramadan. That is Allah's prerogative.