As a "water column equivalent" this is about "30 feet of water" (or 30 inches of mercury). With your tank elevated about 5 feet you have only about 1/6 atm of pressure, or something like 2.5 psi.
If the water in your tank is 5 feet above the toity, the most you can have is about 3 or 4 psi at at the outcome end - with NO FLOW. With 100' of hose, plus some pipe, you can probably sop up the output with a small hanky. Even very low flows eat a lot of "pressure drop" in a hose/pipe.
For public water systems that rely mainly on "static head" to deliver the water, something around 30 feet is usually considered an absolute minimum tower height, and even then pumps are usually used to boost the pressure.
Normal "home water systems" here usually run in the vicinity of about 35 psi. "Regulators" for protecting the plumbing in RVs typically are set at about 50 psi, so that can be taken as a safe maximum for PVC pipe. Garden hose is a different matter. About 35 PSI usually is safe, for a little while, but ~50 psi may make it swell and burst under sustained connection - regardless of what it says on the package.
(We get a fair number of 7" diameter garden hoses - just before they pop - at WVA every year. People put the regulator on the outlet of the hose to protect the camper, but forget that the hose needs protecting too.)
It's possible that the valve in the toity may not actuate at your low pressure, although you still should be able to get at least a dribble. Some such valves incorporate a "trip mechanism" (an over-center device). When the valve is opened slightly, the pressure is what finishes the opening, and when it's forced back shut by the float the pressure holds it shut. If you have a simpler kind of valve, it could work at lower pressure; but a fancy one might have a minimum pressure required to "trip on."
PVC assembly is something of an art. It's fairly simple, but the "adhesive" actually is a solvent that softens the plastic so that it can "cast itself" to the joint. Forcing joints together with excessive force sometimes can force the end of the pipe shut inside the connection, if you've used a lot of goop. If there's a lot of "glue," it can be forced into the joint ahead of the pipe being inserted and can close the joint.
If you can connect directly to the PVC, you should be able to tell if it at least "passes gas" just by blowing into an end. It would appear that your problem is just insufficient "head" to push the water out the other end, but checking the PVC separately might be something to do. I woldn't expect this to be your problem, but one never knows ...
If you have a friendly RV dealer, and can get 12V (DC) power to the tank (or better yet, at the PVC inlet), an RV water pump would be the simplest way I can think of to get sufficent pressure to move the water. These pumps have built-in pressure switches to turn the pump on when the pressure on the outlet side drops below around 15 or 20 psi, and shut off when the flow stops and the pressure pumps back up, usually at around 30 psi. I haven't replaced one recently, so don't know what one might cost, but they're a common replacement so they shouldn't be too outrageous and should be fairly available.