In the May 2003 attacks, militants shot and bombed their way into the three compounds in Riyadh. The assault left 35 people dead, including eight Americans and nine attackers.
The Riyadh bombings prompted the kingdom to launch a sweeping crackdown on al-Qaeda militants, who officials say were behind the synchronized attack.
State media reported yesterday that Riyadh's Specialized Criminal Court issued the five death sentences.
The court sentenced the 37 others to prison terms ranging from three to 35 years on charges of abetting the attacks.