You are about to make a totally crap antenna.
If I'm about to make a totally crap antenna, that would be useful to know too..but I don't mind finding that out for myself either.
Not that you can't make a helical loaded vertical for 10m that is 4' long - that's not hard to do. (Though as Dan
pointed out, it might not be the most efficient solution.) But it is NOT a 5/8 wave antenna, even if it uses
5/8 wavelength of wire - it is still a 4' antenna, and won't be as good as a full quarter wave vertical wire.
The only place I've seen short helical whips advertised as 5/8 wave antennas is for the CB market.
However, I've done as you are suggesting for 15m before, and it isn't difficult to do. There are a couple
rules of thumb that I've encountered regarding the required length of wire for a helical antenna. The ARRL
has suggested about half a wavelength of wire when it is wound with a constant pitch (though this
doesn't take into account the length or diameter of the former, both of affect the resonant frequency.)
The other is that, when the top 1/3 of the form is close wound, it requires about 3/4 wavelength of wire
(which happened to be the case for a particular tapered fishing rod.) Clearly, somewhere in between, you
can find some combination that uses exactly 5/8 wavelength if you want to.
So here is how to proceed. Start with a length of wire - 20' is as good as anything else - and wind it
on the former, with the turns further apart at the bottom and closer together at the top. Set it up
on a pole with 4 radials, each 1/4 wave long sloping down from the feedpoint. Find the resonant
frequency with an SWR analyzer. If it is too low, slide some of the turns higher up the pipe. If it
is resonant too high in frequency, slide some of the windings down towards the feedpoint. Check
the resonant frequency again. When you get it where you want it, add some wraps of electrical
tape to hold the turns in place.