What parts i should upgrade for the following

[balticc]

Budget (including currency): Up to 800EUR

Country: Latvia

Games, programs or workloads that it will be used for: I would like to be able to play Rust, with atleast 60 fps, have Discord open, couple Chrome tabs open, and stream at 720p all at the same time.

Other details (existing parts lists, whether any peripherals are needed, what you're upgrading from, when you're going to buy, what resolution and refresh rate you want to play at, etc): 

Hello, i would want to do the following, while staying in a 800EUR budget if possible, and im interested in what parts i should upgrade.
Current parts; AMD Ryzen 5 1600,  Corsair Vengeance LPX Red 16GB (2x8GB) 3200MHz, Msi Radeon RX 580 ARMOR 8G OC, 8GB, Seasonic Prime Gd 850 850W 80Plus Gold.

 

Attached is my current task manager open with the stuff, exept a stream. 
Thank you!

[Latvian Video]

11 minutes ago, balticc said:

Budget (including currency): Up to 800EUR

Country: Latvia

Games, programs or workloads that it will be used for: I would like to be able to play Rust, with atleast 60 fps, have Discord open, couple Chrome tabs open, and stream at 720p all at the same time.

Other details (existing parts lists, whether any peripherals are needed, what you're upgrading from, when you're going to buy, what resolution and refresh rate you want to play at, etc): 

Hello, i would want to do the following, while staying in a 800EUR budget if possible, and im interested in what parts i should upgrade.
Current parts; AMD Ryzen 5 1600,  Corsair Vengeance LPX Red 16GB (2x8GB) 3200MHz, Msi Radeon RX 580 ARMOR 8G OC, 8GB, Seasonic Prime Gd 850 850W 80Plus Gold.

 

Attached is my current task manager open with the stuff, exept a stream. 
Thank you!

Looks like you would need a new cpu and gpu, as the ram and PSU are good. What mobo do you have?

[Latvian Video]

I have found a Ryzen 5 3600 on rdveikals
And a GTX1080 on SS.lv, because on the used market, there are some good deals
I dont know what your motherboard is, so I dont know if you will need a new one

[balticc]

35 minutes ago, Latvian Video said:

Looks like you would need a new cpu and gpu, as the ram and PSU are good. What mobo do you have?

MSI B450 Tomahawk

 

[Latvian Video]

3 minutes ago, balticc said:

MSI B450 Tomahawk

 

Then you wont need a new mobo. The parts I suggested here are quite good

28 minutes ago, Latvian Video said:

I have found a Ryzen 5 3600 on rdveikals
And a GTX1080 on SS.lv, because on the used market, there are some good deals
I dont know what your motherboard is, so I dont know if you will need a new one