No. This should not be. Are you sure the bridge is straight, or at least sitting how it was installed? A properly installed bridge should create equal string lengths.
Sorry, this is not correct. Due to the construction of bowed stringed instruments with more than two strings, there is always a difference between string lengths on the same instrument.
It is normal if it is only a few millimeters (on my 105 cm 5-string from the outer to the inner string the difference is 5 millimeters, but this is rather extreme).
A difference is normal, because of the bridge curvature and the string angle at the bridge. You only get no difference when the angle on the bridge is zero (or close to zero) or your bridge top "curvature" is flat.
But 5 mm from G to D is a bit much, I think (in my case it was from high C to D, so two string. I wouldn't expect more than 3mm between two strings, rather less.
Measure the string length on all your strings. If E and G don't have (approximately) the same length, then your bridge might not sit correctly. Have a look at the position of your bridge!
On a normal 4-string bass the difference is usually less, because you don't have a string running through the middle of the bridge.
The string angle over the bridge also can differ a bit for basses made for jazz or classical, I was told by my luthier.
The difference also depends on the bridge curvature. I have a rather high one to get a maximum bowing angle for each of the five strings (on my EUB with a highly curved fingerboard for bowing angles of a 4-string on a 5-string), so with less curvature the difference might be lower from outer string to inner string.
Making corrections at the nut seems quite dodgy.
That's true.
If you would make corrections at the nut, the note positions are different on each string, and I'm sure a player won't like to compensate for that when playing.