What are the best approaches to help an older preschooler (~5-6YO age) overcome fear of heights, like going on very high slides/monkey bars/other playground equipment?
One general solution is to start with an "easier" fear to manage (e.g. start with an elevated walkway rather than the slide/monkey bars). Stay with the child and hold their hand. Distract them so they don't realize they're at a height, then slowly draw their attention to it. Encourage them to step up to the railing and reassure them that you're there and will hold on to them and they wont fall, etc. If they have trouble with this, you can start slower (go up the stairs with them and just point out that they're at the same height as the railway) but at no point should you force it (e.g. don't carry the child up to the height, and don't push them towards the edge, etc). If they refuse to approach the edge or have a strong negative reaction, remove them from the stimuli - you don't need more negative feelings being associated with the thing they're afraid of, you need positive feelings and memories.
After the child acclimates to the walkway, move on to something slightly more 'difficult'. The key is slow acclimatization to each new stimuli, always being encouraging and supporting, but never pushing the issue. If you can get them to suggest it, all the better (this can be done by working around the issue, talking about something cool that can or will happen from being introduced to the stimuli, and making them want to see/do it).
For heights (especially at a playground), a good order would be stairs -> walkways/bridges/overlooks -> slides -> monkeybars. For slides, try to go with shorter slides at first and you can either go down with them or stand at the bottom to "catch them". Monkeybars, you can walk along with them while they hang. Also, for slides, they may find it easier to go down covered slides (where they can't see outside) at first. You can later point out that an uncovered slide is the exact same thing but without a roof.
Bear in mind that while you can work with a person to help them overcome their fear of something (or at least be able to manage their fear), you sometimes can't remove it completely. If they're truly afraid of heights, and you aren't having luck, you can see a psychologist, or you can let it be. It wont be the end of the world if they don't play on the jungle gym, and a lot of these fears are passing things that the child will naturally get over as they get a little older. If it truly becomes an issue, and you aren't having luck, seek a professional rather than pushing it and making it worse.
(You don't say whether this is a phobia or a fear. You don't say whether it is a problem that needs to be fixed or if it's just something that you want to fix right now.)
Controlled exposure to the thing that causes the fear is one approach. At all time the child is in control of the actions. You start with activities that are far away from the objective ("playing on high equipment") and work, in tiny steps, toward that goal.
Start by drawing and painting some pictures of a playground. Include some monkey bars and similar. Read or make up a story with this equipment. Go to a playground where they have the equipment, and talk about the children playing on it, but then go do some other play activity, then approach the equipment and talk about it, maybe touch it, and then play on another piece of equipment. Start climbing just a couple of steps off the floor, then come down and do something else.
At each point listen to how the child is feeling. Acknowledge wha they're saying. Do not dismiss their feelings. Then ask them what evidence they have to support their opinions, and talk to them about alternative explanations.