I could have put this in C&V but thought this would work here!
I have a 27" wheel with a 5 speed freewheel. First, what is the maximum # of speed I can go? I kow that my tire selection would be greater if I did a 700c conversion, the canti brakes will work, but what is the largest 27" tire I can use?
Thanks!!

If your frame and hub are spaced 120 mm the most you can fit is an "Ultra 6" 6-speed freewheel. Sun Tour created the Ultra 6 to fit 6 cogs in the same OLD as a standard 5-speed freewheel and it required a "narrow" chain which is the same as current 7/8-speed chains. Unfortunately these Ultra 6 freewheels are now quite rare.

The largest 27" tire you can use will depend more on your frame and fork than the rim but 27x1-1/4" (630-32) tires were very common BITD.

I think my frame is 126mm? As I can spread it a little bit and get my 700c c wheel in.

You seem to not be grasping what the real restrictions are here.

Hub width and rim diameter are completely unrelated.
Maximum tire size is a function of rim diameter and frame dimensions.
Maximum freewheel/cassette size is a function of hub design and frame dimensions.

Measure the nut to nut distance of the hub with the 5 speed freewheel. If it's 126mm, then it's likely that somebody replaced a six speed with a 5 speed freewheel for some reason. If it's 126mm, it's probably spaced for a six speed. Seven speed freewheels had pretty muich the same spacing as the ultra-six speed mentioned earlier. The result was that the seven speed freewheel occupied about the same space as a standard spaced six speed freewheel.

That's a long way around to this: if the hub is spaced at 126mm, you can probably screw on a seven speed and go riding down the road. If it's 120mm, you're stuck with 5 speeds or a 6 speed ultra, probably from ebay.

Or, if it's 120 mm, you can acquire the axle for 126 mm, 6 mm of spacers and make your old hub 126mm. (NB: not all axles are threaded the same and axles used on the same brand hub may be different) You can get something like 2 2 mm spacers and 2 1 mm spacers to make up the 6 mm and then experiment until you get the spacing right. You might need to redish your wheel depending on how the spacing works out and if it bothers you to have your rim a couple mm off center.

I replaced the axle on an old Tipo hub to go from 120 mm five speed to 126 mm seven speed and it worked out fine though I did have to experiment a little with spacer distribution to get clearance for a 14 tooth small cog. Replaced the axle before I built the wheel so re-dishing was not an issue.

Probably not from a tandem.

But spreading a 126mm frame to get a 130mm rear wheel in is usually pretty easy. I've done it on a few steel frames. Some have concern about alu frame spreading, however.

You can get up to 11 speed 130mm wheels.

Are we talking about the Le Tour? It's probably 120mm. Does it have long stays? If so I'd probably not flinch at spreading it to 130.