You shooting paper/steel? If so, those velocities should get you to 1k. If you're worried, try a different powder that doesn't have quite as much case fill maybe?
I took a factory Rem700 ADL Varmint with a 26" barrel a few years back that I tweaked- added a Timney, B&C stock and bedded the action, and added a magwell that took AI mags, but left the barrel and action alone. I was using 178 Hornady Amax with IMR4895 (42.3gr if I remember correclty), Lapua brass, and Fed 210 primers and getting about 2560fps. Took that rifle and load to my first ever precision rifle class, and by the 2nd day of shooting I was ringing the gong at 1k. Felt great! I miss that rifle- sold it when I probably shouldn't have, but everyone on this board has a story about that.
Your 5r comes with a better stock than I added, and a better barrel. Does that 178 you're using have a tip or is it a true hollow point? I'd check the BC against a 178 Hornady with a tipped bullet and maybe give those a try also. With those velocities you should be good, as long as it's steel/paper. You may also try the 168gr- you'll lose some BC but gain some speed. I wouldn't try critters at that range with the .308, but that's just me.
Edited to add: I have a 20" on another Rem700 .308 now...factory 12 twist barrel. I'm shooting the 168 Amax at 2596 with IMR 4895...so you might try a different powder. I've never used 4064, so can't compare, but tinkering is half the fun.