This begins with a listing of all those who have scored a fifty-plus and taken a 5-wicket haul on Test debut:
It is not a long list.
Only 8 instances in Test history. There is only one instance of a century and fiver, which is by Bruce Taylor for NZ v Ind in 1964-65. And there is only one instance of a fifty and 10 wickets, which is by John Lever for Eng v Ind in 1976-77.
Look at the scorecards and you will find something surprising.
These matches were both against India in India and were separated by almost a dozen years. Bruce Taylor had retired in 1973. But one Indian player who had made his debut just before Taylor was still around in 1976 and continued playing until 1983.
He was S. Venkataraghavan, who played in both of these Tests.
And a minor coincidence: There were only three Test players with the surname Banerjee. All of them played in only one Test despite doing fairly well on debut.
SA (Mantu) Banerjee: 5 wickets in the match v WI in 1948-49: http://www.espncricinfo.com/ci/engine/match/62692.html
SN (Shute) Banerjee: 5 wickets in the match v WI in 1948-49, which came close to being India’s first Test victory:
ST Banerjee: 3 wickets in the match v Aus in 1991-92:
However, their arch rivals the Chatterjees and the Mukherjees have not produced any Test players yet. Only a few ODI players.