I think the original Patek denim strap should look great on a 5712. Have just received mine from the Singapore service centre for my 5110p to tone it down and I love it 🥰 ...
I purchased an original PP denim strap at the end of last year. It looks fantastic on my 5712G — the combination of the grey dial and the blue denim works wonderfully. Please find a few shots attached. Take care, and let’s keep the passion alive! ...