DG Bradman, 37 Tests 5,028 runs
AR Border, 47 Tests 3,548 runs
SPD Bradsmith, 34 Tests 3.210 runs
SR Waugh, 46 Tests 3,200 runs
No other Australian has reached 3,000 runs in Ashes Tests. Hobbs (41 Tests) and Gower (42 Tests) did it for England.
Of those players, Bradman (89.78), Bradsmith (58.36), Waugh (58.18), Border (56.31) and Hobbs (54.26) averaged over 50 in Ashes Tests.
Most runs for Australia by batsmen in Ashes Tests
To add a little context, the other batsmen playing for the two teams so far in the present series have the following career Ashes records:
Root 2,208 at 40.14
Warner 2,024 at 38.18
Stokes 1,373 at 36.13
Bairstow 1,208 at 29.46
Special K 1,182 at 42.21
Marnus 778 at 40.94
Head 698 at 41.05
Green 312 at 28.36
Carey 312 at 24.00
Crawley 285 at 28.50
Duckett 212 at 53.00
Pope 157 at 15.70
Brook 132 at 33.00
Root 2,208 at 40.14
Warner 2,024 at 38.18
Stokes 1,373 at 36.13
Bairstow 1,208 at 29.46
Special K 1,182 at 42.21
Marnus 778 at 40.94
Head 698 at 41.05
Green 312 at 28.36
Carey 312 at 24.00
Crawley 285 at 28.50
Duckett 212 at 53.00
Pope 157 at 15.70
Brook 132 at 33.00