Good call on Mark Waugh. He is the Australian with the most first-class runs over a five-year period when county cricket is included.
Leaders from each of the main Test-playing nations:
England. Len Hutton (17 Oct 1946 - 11 Sep 1951): 17645 runs, average 64.16 / 61 centuries. 183 catches / 191 matches, 312 innings.
South Africa. Barry Richards (22 May 1968 - 18 May 1973): 15062 runs, average 58.15 / 43 centuries. 174 catches / 163 matches, 284 innings.
New Zealand. Glenn Turner (17 Jan 1970 - 12 Jan 1975): 13779 runs, average 54.89 / 45 centuries. 148 catches / 172 matches, 294 innings.
Pakistan. Zaheer Abbas (2 Nov 1973 - 1 Nov 1978): 13232 runs, average 53.14 / 41 centuries. 120 catches / 157 matches, 275 innings.
Zimbabwe. Graeme Hick (1 Oct 1985 - 21 Sep 1990): 13027 runs, average 68.56 / 49 centuries. 98 wickets. 159 catches / 137 matches, 219 innings.
West Indies. Roy Marshall (7 Aug 1957 - 3 Aug 1962): 12507 runs, average 40.73 / 26 centuries. 87 catches / 176 matches, 322 innings.
Australia. Mark Waugh (20 April 1989 - 29 March 1994): 12116 runs, average 60.27 / 53 centuries. 109 wickets. 181 catches / 152 matches, 235 innings.
India. Sunil Gavaskar (25 Oct 1975 - 29 Aug 1980): 9513 runs, average 55.30 / 34 centuries. 97 catches / 120 matches, 189 innings.
Sri Lanka. Gehan Mendis (6 May 1981 - 2 May 1986): 7606 runs, average 38.60 / 18 centuries, 38 catches / 123 matches, 218 innings.
Bangladesh. Tushar Imran (30 Jan 2014 - 27 Dec 2018): 5187 runs, average 60.31 / 18 centuries. 21 catches / 66 matches, 99 innings.
Roy Marshall scored one more run than Viv Richards.