There are two ways of getting the front indicators off. One is with removing the front grille and the whole front comes off with the headlights and everything (takes longer, but is much easier), and the other is doing it from the engine bay (no need to take everything off, but much harder).
When I replaced my indicators with clear ones, I did it from the engine bay. By the time I realised the advantages of pulling off the front and doing it that way, I was too far into the procedure to bother.
There are three bolts that hold the front indicator. Two bolt onto the front framework that contain the headlights, and the other goes deep into the front side fenders. Once you have the bolts out, you can slightly push the indicators out forward and you should be able to see how they come out. The plastic can be brittle at times since we're talking about old cars here, so try to make sure you don't snap anything.
Putting the new indicators in is the same as removal. Since you are in NZ and have a RHD car (like me, but I'm in Australia), you will find much difficulty in putting back in the bolts for the passenger side indicator, they're blind holes due to many other components on that side of the engine bay, preventing your head to go deeper in the engine bay to see where the hole is to put the bolt in. Driver's side is easier (at least with my M50, not 100% sure with your 535i) since all there is in the way is the washer bottle, which you might not even need to remove.
If you go the other route and drop the front, I am not sure of the procedure with this (it's in the Bentley manual), but what you will end up with is the whole assembly with the headlights and indicators and the grille on the floor in front of you, and it will be much easier to remove the indicators and replace them, since you will have everything laid out in front of you and you can see what you're doing.
You might find some other board members thinking that my description is rubbish and that they have had success in pulling out and putting in indicators without having to remove anything else, but the truth is at least in my case, that the passenger side indicator is still being held in with only two bolts instead of the required three.
Hope this helps, good luck, and BUY A BENTLEY'S! Use the "Books" link at the top to buy one and support the forum, they are a godsend and you will be doing yourself a huge favour.