When you say slow settling time, do you mean it slowly rises to the correct reading, over-shoots and falls to the correct reading, or bounces around?
I don't have a schematic for that model but I'll throw out some basic stuff based on other Fluke models, maybe it will give you ideas. In DCV mode, the input should be coming in through a 10Meg resistor straight into the ADC. For 5V range, I'm guessing the divider would be in 1/10 mode, meaning the controller will bridge the input via an internal switch to a 1.111Meg resistor, the other end of which is grounded (probably in common with the other values necessary for 1/100, 1/1000, etc.) All these should be on the thick-film resistor array on the LCD side of the board.
I can't quite imagine what sort of fault there would create a time constant slow enough to observe, but hey, have a look at that divider resistor array. If the symptom only occurs on the 5V range, then it seems to be the likely spot for something to go wrong.