All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
Smoking is forbidden; for more benefit on the prohibition of smoking, please refer to Fataawa 354349, 282784, 81589, 81345, 81933, 82827 and 85441.
Also, for more benefit, on the steps to follow to quit smoking, please refer to Fatwa 88467 and 359686.
Taking an oath to abstain from smoking and to pay five dollars against every cigarette you would smoke places emphasis on you to give up smoking and to fulfill your oath.
As for the expiation of the oath, if one does not fulfill it, he has to feed ten needy persons or to clothe them or to free a slave.
Whoever cannot afford one of these should fast for three days.
Allah knows best.