I'm sorry to hear that you are having problems. I checked out your past posts, and found the dxdiag you posted. Your computer is actually pretty good. AMD 8320 4GHz and a Nvidia GTX 960. [up]
Have you watched the temperature at all of the CPU and GPU with a monitoring software? You mentioned crashes 5 minutes in. I could see either the CPU or GPU slowly heating up within that time and crashing. I've used MSI Afterburner, works on any brand card. Here is a link: https://gaming.msi.com/features/afterburner There is a downloads tab a little bit down the screen. There are graphs that the program will show and you can play Planet Coaster for a few minutes and see what the temperature was.
Also open up your computer case and make sure there isn't a lot of dust on your CPU heatsink or your GPU heatsink. If there is you'll need to use some compressed air (those cans work well, or a air compressor but don't hold the nozzle too close or you'll blow something right off your circuit board), or gently vacuum it off. Vacuuming it off has the potential to produce static electricity, so there is a risk with that. Blowing it off is certainly better. Also blow out the inside of your power supply.
Last option I can think of is your power supply. Maybe that is undersized. Do you know what the wattage and brand is? Planet coaster uses your computer to its full potential, and that takes more power, so there is a chance your components need more than your power supply can supply. Or your power supply is going bad. Both options are possible.
When I mentioned heating up, I'm talking about a failure of the cooling heatsink and fan combination to fully take away the heat. This failure could be caused by too much dust on the heatsink, or maybe the fan speed is too low. Some fans can be controlled by a 2 or 3 way switch for low, med and high. Other fans run right off the motherboard, and the motherboard decides the speed of the fans. Often in the motherboard BIOS there is an option for how the motherboard should speed up and slow down the fan.
Normally the new CPUs and GPUs will slow themselves down when they overheat and they won't crash or cause problems. Or in other words, they will throttle themselves.
Another thing that would be good to look into is if you have the newest motherboard BIOS for your computer. Maybe there is a new BIOS that fixes random things.