Affixing a 5kg mirror to an outdoor wall
Depending on how permanent you want it to be and the surface you want to fix it to, a backboard and or adhesive would do the trick.  For less permanent options, build either large or many mirror clips out of some similar wood or pre-set a backboard of the same size and drill and countersink nice screws through the edge of the frame where there is no glass.  If safe frame thickness is substantial, you could recess the backboard 15mm from the edge of the mirror frame and add indirect weatherproof RGB lighting strips in the recess for a nice garish touch.  Mirror clips are probably your best option as they are secure and won't damage the frame and a wide array of aesthetics will be available even if you have to make them yourself.
To elaborate on what I mean by building your own mirror clips:
Here is an image of 3 common types of mirror clip, all far too small for you to use:

You need 3 mirror clips to firmly secure a round mirror.
The first type has a lot of meat to it, so you could build a variety of similar shapes out of wood.  The type of fasteners you'd need depend on the wall you're attaching to.
The second type Would work well in wood as well.  Note the convenient seam shown in the picture.  The bottom clips could be solid and the top clip made in two pieces so the front can be screwed on once the mirror is in place.  With the right design, screws can be hidden on top for a flat face.
The third type would be easy to make in 1/8&quot; thick flat iron.  For the size mirror you have I'd use 1.5&quot; wide.  You can see that a slot is provided for the screw so that two screws can be used to hold the bottom clips without moving and a single screw can be used on the top clip so it can be slid to remove the mirror.  The modification I'd make for a large version is to have the base about 4-5&quot; long and have two slots cut in it so it can slide up and down but not rotate.  1/8&quot; flat is very easy to work with, I built this exact shape just last year for ladder hangers.  To bend round 90 degree bends, use a blowtorch and vise, heat directly the part you want to bend and clamp extra layers of flat or angle to the parts you don't want to bend.  Heat and bend.  For tight 90 degree bends, make sure your vise is firmly mounted to the workbench and the workbench strong, clamp the flat in the vise so the top edge of the vise is where you want your bend.  Apply a small amount of pressure 20&quot; away in the direction you want the flat to bend and use a 3-5 pound sledge hammer to strike the flat close to the jaw of the vise.  Don't try to do it in one hit.  To make the second bend, the jaws of your vise may not be deep enough because of the L shape sticking out from your first bend.  Use a steel block to extend the vise jaw.