Is prayer obligatory for someone who commits grave sins—such as going to brothels—while trying to abandon them, and is his prayer valid in this case?

Adultery is one of the gravest major sins. However, it does not invalidate the prayer if its conditions are met. The one who commits this sin must repent to Allah, perform the prayer, make up for any missed prayers, distance themselves from unlawful acts, and resolve never to return to them. The perpetrator of indecency may be punished in this world before the Hereafter.