Hi Frank,
Fortunately, the GS 5 is very forgiving, so build the coil close to the factory parameters and it will work fine.
This means that most likely any coil between 250 uh and 300 uh will work fine as will other coils with more inductance. If the inductance gets too large then the coil will not work at the minimum delay.
Now, with that said, my favorite calculator is this one:
http://kb9mwr.dyndns.org/n9zia/airind.main.cgi
I use inches rather than millimeters and the .1% accuracy for the best results but I also know that this reading is usually a little high, meaning the real inductance will be less than the .1% but greater than the standard inductance listed. Finally, I will check the inductance using .22 inch for the length or .33 inch and see what difference it makes. The length in this case is actually the thickness of the coil windings.
So, lets say you want to build a 5" coil, so lets use the formula I linked and guess at the number of turns. In this case, knowing it takes more turns the smaller the coil, I will chose 30. Plugging in the proper info and using .22 inch for the length I get the inductance of about 236 uh to 288 uh with the latter the .1% accuracy. Trying the .33in, I get about 233 to 255 uh.
So, I know the windings needed has to be greater than 30 if the formula works well. So, lets try 33 and see what happens. Using the .33 in length, we get the inductance between 273 and 313 uh if .33 is used. Using .22in we get 245uh to 348 uh.
The two different coil length's sort of let me know what I might expect when I change wire types or insulation thicknesses. Use a 300V Teflon wire will give me a higher inductance than that I get when I use a 600V wire. The reason is because the 300V Teflon wire has thinner insulation, thus the thickness is less, making it closer to the .22 length.
The bottom line is, one most likely could use 32 windings or 33 windings and get basically the same results. The final result will depend upon the actual wire used but should be well within the range that will work fine.
So, I would go with the 33 turns and try it since in this case the coil diameter is small. If I were building a 12" coil I might try the 1 fewer turn to try to make sure it would work at the 10 usec minimum delay.
I hope this helps.
Reg