For this hypothetical scenario, let's say Microsoft joined the console race in the 5th gen rather than the 6th, let's say 1995, with disc-based hardware competitive or a bit better than PS1.

How do you think this would change gaming history?

Don’t think it would’ve gone all that well tbh. DirectX only barely became a thing at the start of Gen 5, Microsoft only barely started taking gaming seriously at all (Bill Gates going crazy about Doom taking off with the Windows 95 launch), the team that started Xbox were transitioned from the Microsoft Games Group, which was only established that same year. So there wouldn’t have been any gaming experienced team, and all the studios Xbox was reliant on that first gen would’ve been non-factors.

Probably would’ve been another Apple Pippin or Atari Jaguar lol.

Also, we wouldn't have gotten the Sidewinders! Don't wanna imagine gaming growing up without that lineup lol

We also wouldn't have gotten this sweet little history of PC gaming as consoles were NOT ready for this in the mid 90s. Whole reason this service died was because the team got transferred to the Xbox division.

Microsoft Pippin. Xbox got to where it was because MS worked with SEGA on Dreamcast and even used the DC in focus tests developing Xbox. Was nearly BC and almost had VMU's. Had they tried consoles 5-6 years earlier be some Pippin like thing with maybe WebOS forced into it. So maybe it would be the WebOS version of NUON. At best MS has a CDi at worst, NUON.

that might have very well been their only legitimate chance at a championship.

If they are as aggressive as Sony as getting third-party support, they could've been very successful. At least outside of Japan, that is. I'm skeptical they could've made a splash in Japan.
If they had any online play at all, it would be very primitive. More primitive than Dreamcast or the Xbox we got in 2001.
Globally, they outsell Saturn but finish behind Saturn in Japan.
Even with more of a market split, I still don't see Nintendo winning. People would gravitate towards PlayStation or Xbox for third-party games.

It would make no sense - Sony was not a threat at the time to MS, PC GPUs were just emerging and DirectX was just released in 95, so actual MS push for it to be a standard was not yet necessity for them.

Better question IMO is what would be if MS had more foresight and made something like Steam before Valve did it.

The 5th gen was completely dominated by japanese games and there was no standard for console architecture at that time. So I still think Resident Evil, Final Fantasy and Metal Gear Solid would have the PS1 as their main platform.

Nintendo was still quite strong in the US market in the 5th gen and Xbox probably would sell just around 1 million consoles in Japan. So, I believe it would be behind the N64 and right above the Saturn in sales.

Then we might have an Xbox 5 right now...
No seriously....

One really nice thing about the Xbox 360 was its name. If it had been called the Xbox 2, then the Xbox brand would have appeared to have been one version behind Playstation, which was already on Playstation version 3. It's a silly point, but in marketing terms, it probably mattered. (See the Firefox, Chrome browser version wars since 2010 for example)

Putting a 3 at the end of Xbox and calling it the Xbox 360 cleverly avoided that problem. It was only the second Xbox, but the name made it look like it was competing on equal footing with the PlayStation 3.

If the original Xbox had launched one generation earlier, around the same time as the original Playstation, Microsoft might have followed a much more traditional naming convention: Xbox → Xbox 2 → Xbox 3 → Xbox 4 → Xbox 5

So yeah, in that alternate timeline, we might have an Xbox 2 instead of an Xbox 360, an Xbox 3 instead of an Xbox One, and possibly an Xbox 5 right now.

Perhaps it would have just destroyed the brand a gen earlier. The only reason Xbox failed is because they screwed up massively with Xbox One. Had they stayed consistent with the success of the Xbox 360 instead of pushing down an add on most people didn't want and trying to force always on perhaps Xbox would still be neck and neck with Playstation. Sadly, I do agree it's too late because most of us have our games tied to an ecosystem and it's really hard to switch. I like my Xbox library and I don't want to lose it so most likely I won't switch to PS ever.

Sony screwed the pooch with PS3. Microsoft made other good moves, but Sony's underwhelming and high-cost PS3 was one of the biggest reasons Xbox 360 was so successful. Even years into the PS3's life, third-party games almost always ran better on Xbox 360. 

Xbox One can't really go past 70-80 million units unless Sony screwed up with PS4 or didn't turn the PS3 around. 

There is always a chance Xbox would be out of hardware by now if they did start a gen earlier. That would be 6 or so years earlier in the market and different things going on that might've caused them to just leave the console business.