Help with Shimano parts please.

I have ten year old BMC streatracer SR02 fitted with Shimano groupset. I wish to change the rear cassette and chain and I am unsure if I am ordering the correct parts. The rear cassette shows CS-5700 and has 11t-28t - 10 speed sprocket, I have found this on amazon etc and think it is the current part. The problem I am having is I can’t find any info on the chain so don’t know what to order. I have a twin chainring on the front again a Shimano 105 50f and I think 34t on the inner ring. Any help, would be great .

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