[What page rank is considered a “quality backlink”? Is it >4, >5, does it even matter?]
What one considers a “quality backlink” tends to be highly subjective. Technically, we could consider any backlink that uses relevant anchor text, and passes PageRank, a quality backlink. Some will set standards for PR and/or targeted traffic, both of which increase the value of the link.
Another qualitative measurement might be in the Trust which is based on time in the index as well as TrustRank which seems to be passed in a way similar to PR. However, Trust is not as easy to decipher since you cannot always see when trust has been devalued by the search engines. It seems to be a qualitative factor that is proprietary and carefully guarded by the search engines.