Assuming almost all other factors such as the price point of $200 USD, the 1996 release date, and the first party lineup remain the same, how do you think the 5th gen would have played out had Nintendo opted for CDs rather than sticking with carts?

Some odd part of me assumes that PS would probably get more third party regardless somehow....then again I am half convinced that if Epic, Steam, PS4, GOG, and Xbox all vanished tomorrow and their private launchers stopped working, that we'd see them make a console instead of supporting the Switch fully so maybe I'm just weird.

I think the market was ready for something new. Sony was a very powerful brand in electronics. Possibly *the most* powerful brand at that time. Sony entering the business finally settled the matter - video games were serious, mainstream tech, and they weren't gonna go away. That cachet would have been hard to beat, regardless of what Nintendo did.

PS1 still wins the gen but not by as huge a margin. Sony as a parent company already had the global market penetration to take Playstation to levels Nintendo wouldn't have been able to at the time. Playstation also treated 3rd party developers much better than Nintendo and would've probably still secured a majority of 3rd party games. The only exception being Square.

PS1 would still win. But N64 would sell at least SNES numbers, and PS1 would sell around 80 million or so.

Square Enix would stick with Nintendo. Maybe they would release Final Fantasy VII at some point on PS1, but not at the same time as the N64. Capcom and Konami would likely be more dedicated to Nintendo, but also tip their toes into the PS1 if possible.
The Nintendo 64 DD would no longer need to exist, but the Randnet cart would still be made. I don't know if it would release outside of Japan though. Hopefully the N64 would play audio CDs like the PS1 did.
Animal Crossing may have made it to the Nintendo 64 worldwide, considering the install base would be bigger than it was in reality.

That would cause a chain reaction of events that many people aren't really considering. Final Fantasy and Dragon Quest would stay Nintendo exclusive most likely which means they dominate Japan. Playstation was losing to even the Sega Saturn in Japan until Square having to chose Sony because of no CD option on the N64 radically tipped the scales. 

CD format ensures all the Western support as well (N64 actually still got quite a bit of Western support), with the combination of Mario 64, Zelda: OoT, Final Fantasy VII, and especially GoldenEye it's hard to see them not winning North America as well.

Europe would be the only market with any chance for Sony IMO and even there Nintendo would do very well because of GoldenEye and Final Fantasy VII.

I think most Japanese titles past that would be multi-plat even Metal Gear Solid ... Konami would not be able to ignore an N64 with a much larger userbase and the no.1 position in Japan. Resident Evil and all Capcom games definitely multi-plat.

Sony wouldn't be able to gain traction and wouldn't be able to convince third parties to not put their games on the N64 if it had a perfectly viable CD format as well, we saw during the PS3/360 era they weren't able to convince many devs to stay exclusive because it's too easy to port to the 360 and without them having a dominant market position (ala PS2) the whole thing falls apart like a house of cards.

The N64 even with cartridges outsold the Playstation especially in North America for many months until software droughts (which wouldn't happen with a CD format) caught up to the system and people realized there was only like 1-2 games coming per month as the norm.

The question is how the CD format would have affected the games the N64 had in real life. Long load times would be a real detriment to games like Mario 64, and big open areas like Hyrule Field also benefited from the cartridge format. Another question is how much the N64 would cost if designed to play CDs, but the games themselves would have been cheaper, so that would even out.

Square sticks with Nintendo, so Final Fantasy 7 and most of the other big JRPGs remain Nintendo exclusive and it is Nintendo that gets that big FF7 boost instead of Sony. That alone in my opinion would make the N64 the winner of the generation, as it was the release of FF7 that pushed the PS1 ahead of the N64. Many of the big 3rd party games would be multiplat like Metal Gear and Resident Evil, and they would often be much better on the N64 which was 2-3 times more powerful than the PS1 in pretty much every aspect.

If the exclusives the N64 had in real life stay largely the same I can't see a scenario in which the N64 doesn't outsell the PS1. The PS1 would loose a ton of its momentum and that same boost would just transfer to the N64, and without the storage advantage of CDs the huge difference of power between the two systems would be extremely obvious to everyone. I think the PS1 would sell slightly better than the SNES under that scenario on the strength of Sony's marketing at the time and I think they'd still win Europe, but the N64 would sell 3DS-PSP numbers. Nintendo wouldn't have the marketing chops to push the N64 over the 100 million mark, but the strength of the games would be more than enough to push the system to record levels.

Nintendo would still have had their asses whooped.

Though I personally liked the n64 more. It was just better suited for my age

It would have been closer but PS1 would still have won.

N64 would have had more games.... and cheaper prices on them.

Sometimes storage space might even have held back certain things (textures, sounds tracks ect), and haveing CDs could have resulted in better looking/sounding games. All this together, could probably mean the hardware sales would have been slightly higher too.