The tank is 5 feet higher than the toity, so you have a "static pressure head" of 5 feet for tank relative to toity. This is about 2.5 psig pressure difference. That is NOT enough pressure difference to make more than a dribble come out of the end of the hose.
The absolute pressure at the toity is close to 15 psia though, and the absoute pressure at the tank is close to 15 + 2.5 psia.
You can almost ignore the 2.5 psi difference between tank and toity.
When your pump turns on, it will "suck" the pressure at the pump inlet down by some amount. The amount cannot exceed 15 psi because the water in the hose will boil if the absolute pressure goes negative, and sucking on water vapor doesn't change the (absolute) pressure much. (But don't worry, it won't happen.)
If the pump is a "postive displacement" type, like a gear, vane, or geroter style, it might suck to about 14 or close to 15 psi below ambient atmospheric pressure. If it's a centrifugal or other "dynamic type" pump the drop may be a little less, but should still be at least 10 or 12 psig. It must be capable of sucking to close to 15 psig below ambient (close to zero absolute) in order to be "self priming" on a 30 ft deep well, which is one of the typical (but not universal) design criteria for small water pumps.
If the pressure at the tank remains at 15 psia (atmospheric push) + 2.5 psig static head, but the pressure at the pump inlet is reduced by 10 to 14 psi, the pressure drop in the line between tank and pump will be 10 to 14 psig, maybe plus the 2.5 psig static head, rather than the 2.5 psig drop you had for just the hose laying about. This pressure difference between tank and pump should be enough to supply a continuous inlet feed to the pump. With 100 feet of hose, it may not quite keep up with what would be ideal for the pump; but it should be sufficient for your system to work.
Unless your hose is a really cheap one, or is old and flabby, the 12 - 15 psig "sucktion" is unlikely to collapse it.
The purpose of the pump is to increase the difference between the pressure at the pump inlet and the pressure at the pump outlet. The pump itself is probably capable of increasing the pressure difference from inlet to outlet by at least 70 - 100 psig or more. The 40 psig rating just means that there's a switch that turns the pump off when it gets to 40 psig. The switch most likely references ambient air (15 psi) and shuts of when the pressure is 40 psig = (40 + 15) psia.
Since the pump can pull the inlet pressure below ambient air pressure, the pump inlet quite likely may be a something around 0 to 2 psia, and the outlet will need to be 55 psid above that to produce the 40 psig needed to shut the pump off.
Assuming that your system is all filled and up to 40 psig, when you trip the flush, water immediately flows out and the pressure drops fairly quickly. If your float valve is a "servoed" type, it's the difference in pressure between the inlet to the valve and the exit into the tank that opens the valve fully and keeps it open until the float rises and pushes it shut far enough to "break" the servo.
This difference in pressure from one end of the valve to the other may require a minimum flow since it's the flow that creates the difference. If the pressure in the PVC lines drops too quickly, and if the pump has to suck too hard to try to hold the pressure up, the valve might fail to function as expected. You should still be able to "dribble the toity tank full" but it may be rather slow.
If the pump can't keep up with the flow demanded by the toity, you can "stabilize" the pressure by adding a surge tank. Put a Tee at (or a few inches downstream from) the pump oulet with the side leg pointing straight up. Attach a pressure tight can of some sort so that the water can enter at the bottom and compress air above it in the can. The air will be compressed to the same 40 psig as the water, but can push water back out at near that same pressure for a bit to supplement the flow, keeping the pressure up (perhaps) better than the pump can do alone.
A typical design choice would make the surge tank about 50% larger than the "maximum surge discharge volume." The MDSV in your case would be the amount of water that the toity tank needs to refill - about 1.5 gal for one of the newfangled "environmentall friendly" ones or as much as 7 gal for a really old one. That would imply either about a 2.5 gallon surge can/tank or a 10 gallon one, although you probably won't really need quite that much in either case.
If you put the Tee in when you connect the pump, you can put a stopper in it and decide later whether to add a surge tank. (I'd have on in my camper by now, but I can't find a "5 gallon" space I can fit one into without major re-plumbing.) You can use a hose to connect it, as long as the water goes in and out at the bottom and the air stays on top.
A 5" PVC pipe (~19.6 in2) at 231 in3 per gallon needs to be about 1 foot long per gallon, if that suggests a convenient construction (if I remember my constants close 'nuff).
S(n)ide note: while you're planning all this, I trust you're keeping an eye on how easily you'll be able to drain and blow out the lines when it turns really cold(?). You might want to make that Tee adaptable to connecting a "blowout nipple" that you can pick up at the nearest RV shop - screws into/onto a hose end, with a nipple you can stuff a tire inflation chuck onto. I like the "latch on" chucks for this, since you can let it blow without having to hold it on.