How to know if an Intel processor is a 4th or a 5th Core Generation Processor?

Here is the answer to your question. I had to take screenshots of the text since Intel's website refuses to let you copy and paste text from the table.

6th Generation Intel® Core™ Processor Family

5th Generation Intel® Core™ Processor Family

4th Generation Intel® Core™ Processor Family

Source

You'll want to look up your processor model then look it up on intel's webpage.

Go to control panel and system and it should show you what you have.

Something like

On windows 10, just type in view processor info, and select what it searches for something like

So, in my case I have a 3770

googling that model leads me to intel's ark site (I google intel 3770 ark)

And your generation is on the side under related products

incidentally the first digit does seem to be the model number for 2nd generation and newer core processors.

Alternately cpu-z gives you useful information on your processor and the code name and you can look up the code name