(CNN) -- A California jury Wednesday recommended the death penalty after convicting a man on murder and arson charges in the deaths of five U.S. Forest Service firefighters who died in a 2006 blaze outside Los Angeles. Raymond Lee Oyler of Beaumont, California, was convicted on five counts of first-degree murder, including two special circumstances -- that the murders were committed during an arson and that multiple murders were committed -- making him eligible for the death penalty. Oyler was also convicted of 11 counts of arson and 10 counts of use of an incendiary device in those arsons. Sentencing is set for June 5. Firefighters Mark Loutzenhiser, 44; Jess McLean, 27; Jason McKay, 27; and Daniel Hoover-Najera, 20, died October 26, 2006, during a blaze called the Esperanza fire when the wildfire, fueled by Santa Ana winds, enveloped their engine. The fifth firefighter, Pablo Cerda, 23, died October 31, 2006, at Arrowhead Regional Medical Center, where he had been taken after sustaining burns over 90 percent of his body. Days before being charged in Esperanza Fire, Oyler had been arrested and charged with two counts of arson in a June 2006 fire in the Banning Pass area. The 41,173-acre Esperanza fire outside Los Angeles destroyed 34 homes and 20 outbuildings, mainly in the Twin Pines and Poppet Flats areas, which had been under mandatory evacuations. The firefighters died trying to protect a partially built house in Twin Pines, a rural mountain community.