Fps slumps troubles a rx580 8gb?

I've just gotten a gigabyte rx580 8gb with i5 2400 and 16gb ram to 700w power supply have a mainboard from Acer H61H2 ad. For me minecraft is at 65-55Fps

Minecraft is a very CPU heavy game. Especially with mods or in large structures, this can lead to FPS burglaries due to the i5s!

You have a bottleneck "bottleneck", your CPU slows down your graphics card, I would buy in your place a new motherboard and CPU

Your shortcoming is the i5-2400 … Apart from that, it should be mentioned that an i7-2600k in OC mode @ 4.5GHz is not enough to supply enough data to a RX580.

So should mean that the i5 is clearly too weak.

Which cpu do I need now?

Have no mods and texture packs and Shadermid

Your motherboard can probably be an i7-2600, probably the fastest thing that there's for such an old system… The CPU usually costs less than 50 euro.

Everything else should probably be a new system, probably in the direction of Ryzen 5 2600 + motherboard + RAM.

Already have 16gb ram ddr3

The fits unfortunately in no newer system. There DDR4 is needed.

Have Corsair 16gb ram ddr3

Does not fit yet. New system need DDR4 RAM

It works and does what it should

Whatever. Fine.