I've been riding with a 5-speed freewheel so long I don' t know how to count to six. But with a 126mm rear hub I could go to 6 or even 7. Don't know if it's worth the trouble. Unless I have to drop down to the smaller chainring most of my riding uses only 3 gears, with the very occasional foray into high (48/14).

If I went to a 6 or 7-speed freewheel or cassette would I need a new, narrower chain?

No. And is it worth it? Well, only you can know that.
I'd say don't worry about it, unless you just feel this urge to upgrade. Then, by all means, do it.
-Gene-

Six would still work with a regular width chain but you would need to go to a narrow chaiin with a 126mm spaced 7 speed system. I put togther a 7 speed system for my bike last year with a Maillard Compact Plus freewheel and it shifts beautifully with a narrow Sedis SL chain. which was sold by Campagnolo and Mavic and also re-branded later as a Sedis/Sachs narrow chain. The classic narrow Sedis chain pops up once in a while at eBay if you want to get something period correct, but IIRC, many have noted here that they also have good results with new narrow chains from SRAM too for seven speed systems.

Chombi

Aren't you making it pretty complicated? Brand preferences aside, my experience has been that all currently produced chain designated 5, 6, 7, or 8 speed works fine with any of those numbers of cogs--just don't try to go up to 9, which does require narrower chain.
Or am I missing something?

Last chain I bought for a 6 speed was 6/7 if your putting on a new freewheel or cassette, probably a good idea to put on a new chain as well, a partly worn chain can wear down a freewheel or cassette pretty quickly. Either way, if your happy with the current freewheel, then I would wait until it or the hub starts giving you grief and then decide what you want to do.

Changing the freewheel to a 6 or 7 speed can cause other issues, if you have an indexed shifter then you need to replace that, you need to make sure that the RD has enough room to accommodate the new number of gears. Some can, some can't. Typically though a 5 speed RD can accommodate at least 6 and a 6 speed at least 7, but going from 5 to 7 might be a little tight.

The reason for my question is just the reverse, not whether today's chains will work with older systems but whether my old chain would need to be replaced if I went to more cogs on the rear. I remember when the 126mm space came out, when 6-speed and 7-speed clusters came out, and when "narrow" chains first came out. I recalled that one of them supposed required the new narrow chain. I just didn't remember which one!
Thanks.

No, not making it complicated at all, because I never said that the OP had to use the exact compnent brands I did for my system, It's really up to him to find what he wants on his bike, but he can at least use the group I have as a general guide to find the correct components.
I also just want to make sure that I could back up any suggestions I post here with as much "real working" facts and details that I actually experienced to be as helpful as possible and avoid confusion.

Chombi

Okay, I get it now. The answer is yes, your 5 speed chain will work with six speeds. But if you're replacing your freewheel, it's always a good idea to replace the chain at the same time.