No, that PC is not enough to run Rust.
I see your budget appears to be very low, I'll give you a better suggestion.
At your price range, I'd suggest buying an older prebuilt, (sometimes colleges give their old PC's away for ridiculously cheap prices. You might be able to snag one there) but I'll give you a link to Amazon for one.
I would get this as it has an older I5, which even given its age, should do fine for Rust, and then upgrade it to suit your needs.
You also want 16GB of RAM if possible. The game has frequent stuttering on 8GB or even 12GB
This would probably be a good option, overclock it if possible
You're going to need a GPU. If you want to play it safe and go brand new. An RX 580 would be just fine for playing this game, hell you could probably do fine with a worse GPU. They regularly go on sale for under $200. $200 should be the absolute maximum you buy this card for.
If you have to go used, I'd suggest a GTX 770 if you want to save a bit of cash. The card should also be just fine for Rust, I'd try to snag anything used from the U.S to reduce the odds of being scammed (It's a huge business in cards made in the China area, unfortunately)
The last thing you will need is a new Power Supply, as the one that comes with the prebuilt sucks.

This Specific Power Supply should do you just fine. EVGA makes some of the best stuff out there when it comes to a power supply.

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If you don't feel qualified to do any of the modifications to the PC required, just look up how to do it. There are plenty of great guides out there for that sort of thing. Shoot me a DM if you want to know anything else.

Sure, no problem.

16gb DDR3-1600 (standard stuff, practically guaranteed to be compatible with your mobo)

16gb DDR3-1866 (slightly faster and slightly cheaper!)

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Edit: Replaced second link. Originally linked to incompatible memory, oops!

Cooler Master Hyper 212 Evo CPU Cooler with PWM Fan, Four Direct Contact Heat Pipes https://www.amazon.com/dp/B005O65JXI/ref=cm_sw_r_cp_api_i_MS3tDbN9W885Y



XFX Radeon RX 5700 8GB GDDR6 3xDP HDMI https://www.amazon.com/dp/B07T81CGFY/ref=cm_sw_r_cp_api_i_sT3tDb496Y1V8



Patriot 16GB(2x8GB) Viper III DDR3 1866MHz (PC3 15000) CL10 Desktop Memory With Black Mamba Heatsink - PV316G186C0K https://www.amazon.com/dp/B00453R90W/ref=cm_sw_r_cp_api_i_4T3tDb7TX3RQN

As long as the RAM is the same specs exactly it shouldn't be a problem. If you want to avoid any issues there is a 16gb kit here for $70. I just recently bought it and it's running just fine.

You could also try browsing a place like /r/hardwareswap to see if anyone has a RAM module exactly like your's that you could buy used.

Basically you want to shove together this this this this

https://www.amazon.com/Patriot-1866MHz-Desktop-Memory-Heatsink/dp/B00453R90W

This is the one I was looking at

I have an Asus P8H61-M LE R2.0 motherboard, and was looking at upgrading my RAM.

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Will These sticks work?

Hello, I have an AMD fx-9590 cpu and a MSI 970 gaming motherboard, is this ram compatible? thanks

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https://www.amazon.com/dp/B00453R90W/?coliid=I28Q7NF4J8D7AV&colid=2BYXS9JATXPUT&psc=0&ref_=lv_ov_lig_dp_it

Will this one work

ASUS B450 AMD Ryzen 2 ATX Gaming Motherboard AM4 DDR4 HDMI DVI M.2 USB 3.1 Gen2 (Prime B450-Plus) https://www.amazon.com/dp/B07FKT5CTH/ref=cm_sw_r_cp_api_Z603Bb0JP12FZ

Also is it can i put in the future a ryzen 7

Ram

Patriot 16GB(2x8GB) Viper III DDR3 1866MHz (PC3 15000) CL10 Desktop Memory With Black Mamba Heatsink - PV316G186C0K https://www.amazon.com/dp/B00453R90W/ref=cm_sw_r_cp_api_C903BbKJ3DB01

https://www.amazon.com/Patriot-1866MHz-Desktop-Memory-Heatsink/dp/B00453R90W

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$59.99 for 2x8gb. Just arrived today, brand new still sealed in package. Similar deal should be available on Newegg.

Here's a link to the ram in the picture https://www.amazon.com/Patriot-1866MHz-Desktop-Memory-Heatsink/dp/B00453R90W/ref=sr_1_1_sspa?s=pc&ie=UTF8&qid=1518863673&sr=1-1-spons&keywords=16+gb+ram&psc=1

It doesn't really matter which one you choose, most of them charge around the same.