Can we infer how the Fifth Holy Grail War would have ended had Gilgamesh not intervened? In the Unlimited Blade Works scenario, Gilgamesh intervenes in the Fifth Holy Grail War, kills Berserker, and seizes Ilya. If he had not gotten involved, can we guess based on knowledge from other scenarios what might have happened?
Scenario 1: The Einzberns cheated....again! and thus win

the Einzbern family were at one point holders of the 3rd Magic, Heaven's Feel, which is what the Holy Grail War was original for, reclaiming this magic that at some point the Einzberns lost. Zouken had interest in Heaven's Feel himself because of how his soul was rotting and the Tohsaka only sought to use the Grail to reach the Root.

However the Einzberns have had a somewhat unfair advantage, the Greater Grail's "soul" if you will is that of Justeaze Lizrich von Einzbern and the Einzberns have always had the components needed to finish the war. 


the Lesser Grail which origianlly was a cup but after the 3rd war being the form of a Homunculus similar to Justeaze because if damaged would end the war as was the case in one of the wars and one needs the Lesser Grail to use the Greater Grail to have their wish granted
the Dress of Heaven which can control the Greater Grail


and in different versions of the third Holy Grail War the Einzberns use their knowledge of the System to create a new Servant to get the upper hand, either replacing Beserker with Avenger (which failed horribly) or summoning Ruler to be the absolute authority.

in this answer i explain what i believe the Einzbern's plan was in regards to Ilya. since she's the Lesser Grail if she was killed (being a Master) then no one gets their wish. it's like the Einzberns taking away the ball from the ballgame if things don't go the way they want, but instead of taking the ball away they make every other player destroy it. (it's for this reason Kotomine and Gilgamesh needed Ilya (or at least her heart) for their purposes)

Scenario 2: Angra Mainyu is born and no one wins

in the 3rd war the Einzbern Family summoned Angra Mainyu in the Avenger Class but was quite weak and was killed off early. his death contaminated the Greater Grail.

Kiritsugu concluded after his encounter with Angra Mainyu (talking to him via the radio, TV and appearing as Irisviel) that any wish would lead to destruction, even if Kotomine and Gilgemesh didn't have their own plans and a Master or Servant were able to get a hold of Ilya as the Lesser Grail for their own use and make their wish this would release the six billion curses of the world which Angra Mainyu now embodies.


  The materialization of Angra Mainyu brought forth by truly opening the Holy Grail is an ichor that will consume every human being, 6 billion curses flowing out from the gate to hell. Gilgamesh specifically mentions 5.6 billion curses for an unknown reason. It is a reaper that will strike down all humans equally, an endless darkness that is born from humans and massacres them.


Source: Avenger - Abilities - All the World's Evil

in the Fate and Unlimited Blade Works routes of Fate/Stay Night even before anyone makes a wish the mud from the grail is already spilling and corrosive. in Fate when Shirou fought Kotomine he has to take care to avoid being hit my the mud Kotomine shoots at him as at one point he is grazed by it and is almost succumbed to the curses.

in Unlimited Blade Works Saber stops Rin in wading into the Mud Pool to reach the deformed Shinji because of what it would do to her (if i recall it was Saber's abilities which gave her some protection but it was describing that it was eating away it her)

Sakura as the Lesser Grail

while Sakura is also a lesser Grail thanks to Zouken infusing fragments of the one from the 4th war into his Crest Worms that are inside her Sakura's connection to the Greater Grail is to that of Angra Mainyu itself. 

before she realized she was The Shadow it was already consuming people and Servants and unleashing Saber-Alter and Blind-Berserker. while Zouken might have been able to control Sakura for years in the end The Shadow wasn't under his control. it would have only been a matter of time before it controlled Sakura as the ribbons that's seen on The Shadow make up Dark Sakura's dress which was then used to bind her after her's and Rin's fight near to the end of Heaven's Feel.