Giving the OP the benefit of the doubt, I used the word "adapt".
Since we don't know which, I presented options for both.

I appear to be wrong, it looks like the largest is a 21T, not a 24 as I had originally thought.

By my count I've actually got a 13, 15, 16, 17, 19, and 21T freewheel. No wonder that hill climb was rough.

Well, you will probably notice a lot of difference if you get a 28T for the low gear! Especially if you can also add the 39T small chainring.

I used to ride a 14-21 5 speed and then eventually moved to a narrow 6 with 13-24 and more recently to a 13-26 7 speed. That helps keep a cadence on climbs!

Otto

Yeah, going from a 21 to a 28t is a huge difference. 39x28 is plenty of gearing IMO if you are young and relatively fit.

BTW, that is clearly a cassette, not a freewheel. Should be reasonably easy to swap some cogs.

RE the toe clips: yes, I saw that some pictures had them and some not. If they don't fit they don't fit. You could acquire longer clips, or space them as mentioned. However, IMHO, you won't get the full benefit of toe clips without the cycling shoes that used to go with them. Realistically, those are no longer available. Some 'touring' shoes would be helpful though. But, clipless is a more logical way to go. All the benefits of clips and straps and cleated shoes, but way more comfort and convenience, This bike is from the transitional period, so they won't look out of place.

OP, I suggest you grab that Hyperglide cassette I linked from Ebay. The tooth counts aren't posted, but it looks to me like 13-14-15-17-20-24-28-32. If I were you, I would use your original 13, 15, 17 and the HG 20, 24, 28 sprockets to get a nice progression. If your RD can manage the chain wrap, another nice one would be 13-14-16-19-24-32.