Yesavage was taken out after seven innings of work, giving up just one run on three hits and no walks in one of the best World Series pitching performances in recent memory.
The Fall Classic now heads back to Toronto for Games 6 and 7* (if necessary) as the Blue Jays hold a 3-2 series lead - just one win away from their first World Series since 1993.
Game recap
Blue Jays 2-0 Dodgers
The Blue Jays made history on Wednesday after becoming the first team to hit back-to-back home runs to start a World Series game.
Davis Schneider got the party started with not only the first home run of the game, but his first home run of the entire postseason on the very first pitch of the game.
Vladimir Guerrero Jr., who already set the franchise postseason record in home runs, sent his eighth out of the park just two pitches later off of Dodgers starting pitcher Blake Snell.
Blue Jays 2-1 Dodgers
The Dodgers would respond in the bottom of the third inning with a Kike Hernandez home run - his first of the postseason. But that's all they would get during Game 5 of the World Series as Blue Jays starter Trey Yesavage was absolutely dominant.
Blue Jays 5-1 Dodgers
Blue Jays' Ernie Clement would add on with a sac-fly in the top of the fourth inning after teammate Daulton Varsho hit a triple.
Then, the Blue Jays added insurance en route to a Game 5 victory when Addison Barger scored on a wild pitch to make it 4-1.
It was the second wild pitch of the inning, with the first from Snell and the second from Edgardo Henriquez, who replaced Snell with two outs in the seventh.
Snell finished the night giving up five runs on six hits with seven strikeouts and four walks.
Then, the league-leading hitter Bo Bichette did what he does best and drove in the fifth run for the Blue Jays with an RBI single off Henriquez.
After walking Alejandro Kirk, Henriquez would be replaced by Anthony Banda, who would get the Dodgers out of the inning.
Blue Jays 6-1 Dodgers
Bondra would throw the Dodgers' third wild pitch of the game after giving up a single to Ernie Clement, advancing him to second base. Barger would ground out to move Clement over to third before Isiah Kiner-Falefa brought him in with an RBI single.
The Blue Jays finished the game with nine hits, also going 2-for-7 with runners in scoring position.
Los Angeles would record just four total hits, two coming from Teoscar Hernandez and the other from Will Smith (plus Kike's homer), as Blue Jays relievers Seranthony Dominguez and Jeff Hoffman would toss two shutout innings.
The Dodgers finished the game going just 0-for-1 with RISP.