Not sure if this is the right place to post this either, but I might be able to offer a little advice.
Sounds like damp has affected the display connector or the cable is damaged, or the cables in the hinge are damaged.
Depending on how adventurous you are feeling you might want to start by cleaning all of the connectors with isopropanol (or even a drop of vodka) with a cotton bud.
Be safe.. There are a couple of risks here, first and foremost there is a large capacitor attached to the flash, and it can give you a nasty shock if you are careless when you have the camera disassembled. I don't have an S5IS, but looking at that video, I don't think you are at much risk, since the capacitor is covered by some plastic screening, but take care anyway.
The second risk is that you do more damage to the camera when you have it apart. To replace, you will need the correct sizes of jewelers screwdrivers, small tweezers and pliers, and a magnifier or 3x reading glasses may help you with the fiddly connectors. Use the wrong tools, and you will wreck the screws and/or the cables.
Gently wiggle the various cables with an insulated tool (for example a toothpick) as you take things apart, to see which one cause the display problem to change, chances are that is the one associated with the issue, however don't use a metal tool as you may short out something and release the magic smoke (invariably fatal to the camera), or touch the flash capacitor... which is a very nasty experience, think electric fence x 100.
Safety tip... Keep your left hand in your pocket if prodding about in a live camera, to avoid a potentially fatal zap from one hand to the other (this is the voice of experience here, you zap yourself entirely at your own risk
don't say I didn't warn you).
Important. The capacitor remains charged for several hours even once the batteries have been removed, so always assume it is charged.
Here is a video of the procedure to take it apart.
Canon S5 IS hinge replacement ... this shows the hinge replacement, probably the most likely cause of the issue you describe, based on the fact that the screen changes when flipped.
At about 4:15 in the video you can see the internal brown LCD screen connector at about the 2 o'clock position on the back of the assembly, this is also a possible source of issues, look at it very carefully, if it looks like there is damp in, or on it, remove the connector (this requires extreme care, don't force it), inspect the connector, and clean the contacts *carefully* and re-insert. Usually you need to release the cable by *gently* operating the release mechanism, so inspect carefully, and google for instructions if in any doubt how it works (or post a good image here and I will advise).
If the screen itself is damaged, (even the smallest crack can cause the kind of issue you are seeing), you should be able to find a replacement on ebay... usually the screen is a separate item, and often supplied as just the glass and cable, so it is very delicate and requires extra care when handling to avoid fingerprints and dust getting in to it (which will be visible when you re-assemble and switch it on). Replacement requires you to disassemble a little further than is shown in the video, and also to *carefully* "unpick" the sandwich of LCD, screening can and back-light. Typically ebay seller...
http://www.ebay.co.uk/itm/LCD-Screen-Display-Fit-Canon-PowerShot-S5is-S5-/380250584832 I cannot vouch for them, buy at your own risk, and note that this is just the glass screen for sale here, not the whole rear screen assembly. You might get a good screen in a lens damaged S5 for less.
Good luck.
and remember do everything slowly, take notes of which screw goes where, they are all slightly different sizes, lengths, colours and threads. A tip here is to use a small box with strips of double sided tape to sit them on, stops them rolling away, and allows you to close the box and return once the inevitable interruption to your flow has been dealt with. To re-assemble, reverse the process.
