The ZF 5HP24 transmission used in M62-engined E53s has the following forward gear ratios :

1st = 3.571429
2nd = 2.200000
3rd = 1.504673
4th = 1.000000
5th = 0.803738

The 4.4i has a final drive ratio of 3.6364 (40/11) and for the 4.6is it’s 3.9091 (43/11).

Tyre rolling radius for the 4.4i = 365mm (235/65 R17, 255/55 R18, 255/50 R19, etc.)

Tyre rolling radius for the 4.6is = 361mm (275/40 R20 F & 315/35 R20 R)

Hence, in 4th gear the 4.4i is geared at 23.5mph/1000rpm and the 4.6is at 21.6mph/1000rpm

In 5th gear, the gearing is 4.4i = 29.3mph/1000rpm and 4.6is = 26.9mph/1000rpm

Consequently, your 4.4i engine would run at 2977rpm in 4th gear and 2393rpm in 5th at exactly 70mph with the torque converter fully locked (bearing in mind that your speedometer will read fast and tyre rolling radius varies by 6mm from new to worn)

If your engine is running at 2600rpm at an indicated 70mph then your transmission is in 5th gear but it sounds like your torque converter lock-up clutch is slipping

Phil