What is "reasonable" accuracy for a hunting rifle?

[PJGunner]

"I cleaned the rifle barrel after every five shots, and between when I used different types of ammo."

That could be part of your problem. Some, if not all barrels need to be "seasoned" after cleaning. To get a barrel shooting right again can take as tqo or three shots to as many as ten. I take my load work ups very seriously. I'f I'm starting out with a totally clean to the metal barrel, I'll run off about five shots with some left over ammo to foul the bore.
and let the barrel cook down. Then I run my shot strings giving about a two minute weight between shots if It's a cool ca, On hot day I can wait as long as 10 minutes between shots to get decent results. In my particular neck of the desert it's either do it like I do or don't shoot at all. Why? Because I've done more than a few desert Mule Deer and a couple of Coues deer hunt and the temps run anywhere from maybe 70 early in the morning to near 100 by dusk. You learn to skin and gut quickly if you want to save the meat.
for spits and grins, let's say you work up a load in 90 degree weather. Maybe it goes below freezing on the hunt. I did the final sight check here in Tucson at 95 degrees. When I got to New Mexico, Raton to be exact for and elk hunt I double checked my sights at the NRA rnge and they didn't need ant tweaking. Two hours into the hunt on the private ranch where I was hunting I had a nice fat juicy cow elk on the ground.

From load work to hunt finish that rifle and the back up rifle I brought just in case never got cleaned until the day after I got home and the meat in the freezer. The guns are just fine. FWIW, a custom Mauser in .35 Whelen running 225 gr.TSX and a custom Mauser in 30-06 as back up running the 165 gr. Nosler AccuBond..
PJ

 

[Aussie Wanderer]

I've skim read most of the replies and PJ noted that he waits for his barrel to cool down. I was actually wondering how fast you were going through the strings. We have a couple of rifles that after the first three shots will open up a little, unsurprisingly all are magnums. Time between shots might help too.

 

[PJGunner]

I've skim read most of the replies and PJ noted that he waits for his barrel to cool down. I was actually wondering how fast you were going through the strings. We have a couple of rifles that after the first three shots will open up a little, unsurprisingly all are magnums. Time between shots might help too.

Well, while I really don't like the fairly long waits between shots when it's110 in the shade and there ain't no shade you do the best you can.

I'll admit it's not perfect but I try to come as close to a cold bore first shot with each round of the test load. That's why, especially in the summer, I take about a half dozen rifles to work with. When it's that hot, the closest you can come is to whatever the current ambient temperature is. FWW, today's high is forecast to be109* F. We sometims get highs in the upper 80s into the 90s in Marcch and as late as October or Novemebr. Rarely, and but it does happen that we'll get snow around December and January. I've lived here for the last 47 years and it has only snowed maybe five or six times. It doesn't stick on the ground other than a very short time.
PJ