How long is a piece of string? It depends.
How many LUTs are typically required to implement a simple CPU?
How big is your CPU? How many features does it have? multiplier? divider? predictive branching? What frequency does it run at? What brand of FPGA? What family within a brand of FPGA? Even which version of the toolset for that FPGA.
All these factors affect how much logic the CPU will require, and how much memory and logic resource it will require.
Is 5963 LUTs a lot?
Maybe, maybe not. Again it depends on your design. For a massive complete system it is tiny. For a little CPU and a few peripherals it could be more than enough.
Now that's out of the way, a better question would be how do I go about checking?
To start off, pick a vendor - Altera/Intel? Xilinx? Lattice? etc. Up to you.
- Pick one that you like the toolset (development environment)
- One for which your desired electronics supplier has good stock.
- Compare also prices - you probably want to go with an entry level series unless you have need to features like DSP and Gbps transceivers.
- Pick one that you have or can get the tools to program.
To be honest it doesn't really matter which you pick, but you need to pick one.
Download and install the toolset for that vendor. These a $%£& huge packages, so you only really want to be installing one, hence picking an FPGA family first.
Once you have the toolset installed, create a project. Many allow you to create projects that target a specific series of FPGA as opposed to any specific device. If not, simply select the largest device in the family that you have chosen - it doesn't matter if you don't go on to use that device at this point.
Design your CPU in your chosen HDL (*Verilog, VHDL, etc.). You can download IP cores for the internet (though be wary, many are not verified and in many cases more hassle than they are worth), or try out the vendor specific IP that comes with the toolset (some may require pricey licenses).
Test compile - this is the key point. This is the point at which your question is answered. The FPGA toolset will tell you how many resources are required for your design. At this point you can then change your target FPGA to a smaller and cheaper part in the selected family and recompile to check that it still fits.
At this point you are ready to start tailoring your design to the chosen FPGA. You can start looking at pin-outs and hardware resources (DSP, RAM, etc.). Make pin assignments and compile an actual design - this can be where the tools bite back, it's very easy to select a pin that cannot physically be used in the way you want (e.g. feeding clock into non-dedicated pin, using programming pin for IO, we've all done it).
Only once you have a synthesisable test design do you even thing about designing hardware or ordering parts.