print design - How do I edit my CMYK greens to output as brightly as possible?

Converting my photoshop work from RGB to CMYK to send to print. Found out today that RGB has a much broader and vibrant colour array than CMYK.

Trying to edit the values, saturation, brightness, exposure etc. to make my greens look even REMOTELY close to what I want. All I've been told is "you'll never get CMYK to look like RGB" which is fine, except for nearly every magazine and booklet I have at home has the vivid, vibrant greens and blues I want. How?

It's very frustrating especially seeing as I've only learned this 3 days before I need to have it printed.

I've searched the values for lime green with CMYK with were C - 70 & Y - 100 (in reality I want it a bit darker than that) but it just comes out as a murky khaki colour on my screen.

The green on the left is the colour I get in RGB. The other two are the colours I've managed to replicate. However, I have at least 6 brochures/booklets at the side of me which all have that bright green colour on the left in them. So why can't I get that colour? Is there a difference between screen and print due to the way the models work? I'm a novice to this and it's all a bit confusing! Thank you