6.5x55 Swede has been around for 130 years. Not flavor of the year like 6.5 creed and 6.5 PRC
I would not say the Swede will do what OP wants to 500 yards, but certainly 300 all day. 140 grain spitzer for deer and bear. 160 grain RN for moose.
Recoil is light even when I load mine hot.
If I were to go for a 'modern' 6.5 it would be Creedmor over PRC but then I would still limit myself to 300 yards for hunting
To 500 yards the .308 would be 'adequate' for hunting IMHO