I would like to upgrade the rims from 27 x 1.25 to 700c. I would like to use the same 5 speed cassette on the 700c rim (see pic below). Would any new 700c cassette hub rear wheel work with that cassette ? Also would there be any issue with the chain lining up with the cassette on the 700c wheel ?
What you have there is a freewheel, not a cassette. The difference is a freewheel combines the freewheel ratchet mechanism and sprockets and mounts on a large diameter thread on the hub; the freehub/cassette system puts the freewheel ratchet mechanism in the hub and the sprockets slide on a splined freehub body. See here for in depth explaination.
You probably have a hub with frame spacing of 120mm (see here). Modern 700c road wheel have a spacing of 130 or 135mm.
What you will want to do is get a wheel with a 120mm freewheel type hub onto which you can put your existing freewheel (or a new one), but with a 622mm diameter rim (700c) rather than the 630mm (commonly called '27 inch') you have now.
I assume you know you will have to find long-reach rim brake calipers to deal with the difference between rim diameters.
Let's clarify some terms.
- A "rim" is the hoop at the perimeter of the wheel, which you mount the tires on. It sounds like you're talking about replacing the entire wheel. It is possible to cut off the old rim and rebuild the wheel with new spokes and rim, although probably more expensive than just buying a stock wheel.
- A "cassette" is a cluster of gears that slides onto a "freehub body": this is a freewheeling mechanism and splined cassette carrier that is part of the hub. What you've got is a "freewheel," which combines the gear cluster and the freewheeling mechanism; it screws onto threads on a suitable hub (freehub-hubs and threaded hubs are incompatible).
Threaded multi-speed hubs are still around, but they're older technology.
Changing your wheels will involve a few things:
- Brake reach. 700C rims are slightly smaller than 27" rims (622 mm vs 630 mm). So you'll need to readjust your brake pads to fit the new brake track on the rims. If your pads are already at the bottom of the brake arms, they won't be able to reach, but if you've got 4 mm of margin, you should be OK.
- Rear triangle width. Your bike probably has an "over locknut distance (OLD)" of 126 mm. You'll want to make sure that your new wheel matches that (the front will have an OLD of 100 mm regardless). As far as I know, there are no freehubs with 126-mm spacing, so you're locked into using a threaded hub unless you want to spread the rear triangle.
- Gearing. You could probably reuse your old freewheel, but I'd bet that it's due for replacement. Change the chain too. Since you almost certainly don't have indexed shifting on that bike, you could go to a 6-speed freewheel if you want. But I don't think you'll have a problem with the chain "lining up" because that's a problem of indexing.