5N silver, well that's pushing it from a non clean room environment.
You will need analytical grade water, acids, impeccable glassware washing routine and glassware washing chemicals fit for a lab, dedicated glassware washer.
Even getting 4N from home is a massive effort, just quietly, unless you see the icp test results stating a ppb for every element I would not accept a say so unless a complete lab report is made. I have seen the generalisation of lab reports, people claiming even 4N I do not buy into that sort of caper.
Then when you get over that hurdle for 5N or even 4N, what furnace are you using, even the zircon from refractories, furnace lining, crucible lining, carbon from the torch, contaminants from the melt dish and borax lining will find their way into your metal, just pouring silver into water will produce detectable contaminants at 5N.
The stainless bowl if using electrolytic cell will leave traces of molybdenum, iron, chrome, etc, the copper used to cement out will have its own trace elements detectable, all this even if you use the correct grade of stainless steel, this is something impossible to rid no matter how many times you run it through the cell.
Same goes if you use Agcl method, salt contaminants, Sugar, etc. Hcl needs to be analytical grade, caustic too and the list goes on and on.
Not trying to deter you from trying, take it from me, a guy who does take every effort and measure, when doing icp for ppb even things you thought are not possible as contaminants will show, its a huge learning curve, but a worthwhile one for me, the process really gets into the nitty gritty and reveals a great many limitations of what is feasibly practical and possible from home refining, also reveals to yourself your own work ethic and cleanliness.
