No, I don't mean it needs to be more than 5%, I mean the 5% increase is literally too small.

After gaining and activating the perk, the cycle speed on my missile launchers went from 0.87 seconds to 0.86 seconds. A speed increase of 0.01 seconds is NOT 5%. Either what you are calculating as "reload speed" is very counter-intuitive or else the math has dropped a decimal place somewhere, because turning on that perk increased my reload speed by 1.1%, which when you take into account rounding errors in the display means it probably only increased it by .5% and the rounding made the numbers look better than it actually was (which was still only 1/5 of what it should have been). Had it worked as expected, I should have seen recycle time drop from 0.87 seconds to 0.83 seconds.

And I doubt the issue is a misunderstanding of what reload speed is supposed to affect, because the increase in reload speed for mining laser perk works exactly as expected... so unless you calculate reload speed very differently between mining laser turrets and other turrets, there's a problem in the math calculation somewhere.

[edit] The turrets in the earlier comment were epic laser beam turrets, NOT missile turrets... so to minimize the effect of rounding errors, I changed to my basilisk so I could use a low end regular turret, mining turret, and missile turret and compare numbers. Here's what I got.

Mining turret recycle time: 12.27 sec, Missile turret recycle time: 5.25 sec, Plasma turret recycle time 2.25 sec

After 1 mining perk (+5% mining turret speed):

Mining turret: 11.64 sec ( 5.1% improvement), missile turret: 5.25 sec**, plasma turret: 2.25 sec**
** unchanged, as expected

After 1 weapon perk (+5% turret reload speed):

Mining turret: 12.17 sec ( 0.8% iimprovement), missile turret: 5.21 sec (0.77% improvement), plasma turret: 2.23 sec (0.89% improvement)

The only conclusion I can see is that either you consider turret speed and turret RELOAD speed to be two different concepts, or there's a math problem in the weapon perk.