Although I understand many of the concerns about your offered treatment at this particular office periodontal disease is a "silent disease" that nearly 70% of american suffer from. A simple cleaning (prophy) without a deep scaling and root planning will not clean the bacteria/plaque that has created the deep pockets around your teeth. A full mouth probing will only determine what your periodontal class is. Any pockets around a tooth that is 5 mm or greater and that bleeds when the dentist probes in general means that the specific area will need a deep scale to remove the harmful bacteria and hopefully get the pockets back to 3 mm or less. There are one or two exceptions on that but I will let you do your own research.
Please also check out the ADA (Ameican Dental Association) website to learn how periodontal disease is diagnosed by dentists so you can make an informed choice on your treatment and not just go with the cheapest option.
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