Which test to compare proportions?

I need to compare is there is a significant difference on how my products attract old and new clients in two different ways. I have 250 old clients and 50 new clients. So in my base ~17% are new clients.

Way one, comparing between products: 5 of my new clients and 37 of my old clients bought product A, that is 10% and 15%. 10 of my new clients and 20 of my old clients bought product B, that is 20% and 8%.

I would like to know if there is a difference in the preferences between product A and B for new and old clients.

Way two, comparing against overall numbers: I got 42 total purchases for my product A, 12% of them done by new clients. I want to compare this against overall base (~17% are new cleints). So I want to understand is that product attract more old clients or the difference is not significant ebough to make that claim.

Which tests should I use in each case? I use R

Thanks in advance!