Change the 5/8 wave as having a higher impedance than the 1/4 wave too. The 5/8 wave antenna has a lower impedance then the 1/2 wave end fed but is still much higher then the 1/4 wave.
what Shockwave says is backed up by the fact it needs a loading coil which is tapped at some point between the top of the coil (1000 or so ohms) and the base of the coil ( 0 ohms), at some point inbetween it must be 50 ohms which is exactly where you tap the center conductor of the coax too, which is why the correctly designed 5/8 wave shows good match to 50 ohm coax.
the end fed halfwave with an end impedance in the couple of thousand ohm range is tapped exactly the same way.
the radiator in both is made slightly shorter than a full 5/8 or 1/2 wave to counteract the reactance introduced by the addition of the impedance matching coil.