you should not have any voltage at the fuel sender.
LMAO......Okay, I couldn't let this one slide. I have to ask then, how do they work without "any voltage at the fuel sender"? Hmmmm....
Okay so OP,
As Ding says, the sender's resistance (Rs) varies from around 33 ohms full (Rsf) of gas to 240 ohms empty (Rse) of gas.....The gauge's "S" terminal has an internal resistor (Ri) that is tied to the Ig, terminal, when the key is on, 12V (Vs) is applied to this internal resistor and divided (a voltage divider for the techie's) between this internal resistor and the sender's resistor, this sender resistor is wired as a rheostat, again, as Ding says.
The internal resistor is fixed at about 140 ohms....
On full the sender's pink (or "S") wire(at the gauge or sender, same wire) should read around....
Vs/(Ri + Rsf)*Rsf = 12V/(140+33)*33 = 2.29V
On empty the sender's pink (or "S") wire(at the gauge or sender, same wire) should read around....
Vs/(Ri + Rse)*Rse = 12V/(140+240)*240 = 7.57V
Sounds like your tank, by your voltage reading of 5V that SHOULD be present at the sender, your tank is around 1/4 full.
Guessing needle on gauge is stuck/bad meter movement.........