Who will win the Fifth Frontier War?

The Llellewyloly. The revolution will begin as the Imperium is distracted. The Marches will fall under the iron hand-leg of the dandelion.

(Silly answer out of the way, I'd like to see a Zhodani win, mostly because I'd find it interesting to see a forced rexamination of their motive on the part of the Imperium. What does the average Imperial know about the Zhodani beyond "they're the bad guy, as I was taught"? We know that, telepathic artefact business aside, the Zhodani are motivated by fear of Imperial expansion and not expansionist desires of their own (for the most part). Basically, I think a Zhodani victory would throw up more surprises in regards to how the factions relate to each other -- especially if, thanks to telepathic artefact business, the Zhodani actually *were* aggressors here, and are dealing with their disquiet over it. The Zhodani, I think, won't know quite what to do with their victory the way the Imperium would, which promises some fascinating opportunities.)
It would be interesting if the Vargr managed to take hold of the Corridor and cut off Deneb and the Marches from the Imperium.
The Sword Worlders and the Zhodani could launch their offensives and take some ground.
The Imperium would have to regroup, but the Ine Givar could launch a full scale operation and Arden could make a power play.
Maybe even the Marches and Deneb would think about secession.

And the Travellers could be contacted by a Hiver Manipulator, who has "The Plan" that wants to shape this chaos into something.
Seven won by there being a Fifth Frontier War in the first place. It shows the true survivor of Secrets of the Ancients as the original plan was to foment conflict between the Zhodani and Third Imperium. The time of the new God Emperor is nigh
If my players (and a certain Hiver behind the scenes) have anything to say about it, it'll be the Gimli Star Alliance...
I'm also in the "won't touch antisocial media" camp.

But as far as the outcome? How about a scenario in which no one really wins - but not because it just ends up as another stalemate with everything magically going more or less back to how it was afterward (per tradition), but because the war ends up producing mixed and unexpected results for everyone concerned? Gains here, holds there, losses in other places, a surprising number of which are the we-really-didn't-see-that-coming variety, so the map and the whole region end up in a state that no one would have anticipated going in.

It would be far more interesting (and perhaps more realistic, given how large-scale, protracted wars tend to set unexpected dominoes falling) than an "X won, Y lost" result, and it would also allow for a soft reset and complete re-exploration of the region in a book (or books) set afterwards.
“War does not determine who is right.” It only determines who is left. - Often attributed to Bertrand Russell

That said, there will be profiteers at all levels. If they play their cards right, the Travellers might be among them.
DAX: As the 34th Rule of Acquisition states, "Peace is good for business".

QUARK : That's the 35th Rule.

DAX : Oh, you're right. What's the 34th?

QUARK : "War is good for business". It's easy to get them confused.
They would hang profiteers. It'd be quicker than letting the angry mob take them.
Here's a thought.
before the OTU FFW the set up was a pretty corrupt and decadent Imperium. The Ine Givar could easily be seen as freedom fighters and there appears to be considerable discontent between Spinward Marches worlds and any expansion of Imperial authority.

So what if during the FFW the Ine Givar stage uprisings on multiple worlds and other worlds break with the Imperium to form their own trading blocks.
I liked the corrupt, ossified Empire that had political prisons and lying officials and not enough Navy to go around. It made Strephon the not very effective reformer make a lot more sense. And it made the Marches a lot more frontier-ish than they are often portrayed in later work.

You know, the one with the hypocritical MCr1 reward for finding out what happened to the Imperial Senator that just happened to have been arrested by the Imperium and stashed in a political prison without trial.
I'd like to see the Imperium sent reeling. Maybe in the Marches after an armistice their is a (cut off) Regina based polity, several worlds under Zhodani, SW and Vargr occupation (all of whom are frantically reverse engineering captured Imperial technology)and a broad movement on many worlds for more rights/outright independence. In Deneb there is a massive political crisis as the sector sees itself as now on the Zhodani front line as well as the Vargr one and recriminations over allocation of Naval resources explode.
In the Trojan Reach the Aslan see Imperial weakness and prepare to overrun the reach and carry on into the Imperium.
Te Solomani and the K'kree sense Imperial weakness too
In fact the only reliable possible allies are the Hivers. They just have a few ... suggestions ...