Is there a connection of recent 4 CM solid kidney mass (will be removed next week) and thyroid cancer 5 years ago (papillary with follicular variant)?

Maybe. There may be a link, but the data at present are not completely understood (and seem contradictory in some papers). It is worth talking to a genetics expert. http://www.ncbi.nlm.nih.gov/pubmed/10843148 http://www.Ncbi.Nlm.Nih.Gov/pubmed/20465534.
Yes. Patients who have survived thyroid cancer have an increased risk of suffering a second malignancy, including renal cell carcinoma. A higher prevalence of genitourinary and kidney tumors has been reported in women with differentiated thyroid carcinoma.This association could be related to the specific treatment of the disease or to a genetic predisposition.