What do you mean? This problem has already been solved and is just a case of miniturisation which history has shown the industry can do very quickly.
5 Years and there will not be a 'headset' on sale anymore. It will all be normal sized glasses.
For example, consider field of view, which is a critical measurement of these displays. Typical specs are 120 degrees for headsets, 40 for glasses.
Headsets also perform very high performance rendering compared to glasses. The tiny <1Wh batteries in glasses are insufficient for that amount of work.
Glasses can't be expected to compete with headsets, much less eliminate them from the market entirely within a few years. It makes more sense to think of VR headsets and AR glasses as completely unrelated product categories.
I think you are short sighted (haha!) to think that headsets and glasses are different categories, and that headsets are not just a preliminary research phase to things in the future like smart contact lenses etc.
Contact lenses having the capability of a headset? That's just magical thinking.
100 years ago, the mobile phones in our pockets would have been magical thinking too.
You could add more cameras and lidar for depth, yes, but then you'd also need a display for the other eye, and you still wouldn't be able to do immersion because your displays are transparent and have a tiny FOV, and you're also not doing passthrough, so why do you need the cameras again? And so on.
Sadly I think you are vastly overestimating the rate of progress here. Quest 2 came out 5 years ago - in those 5 years we've shrunk headset volume by about half (mostly due to pancake lenses). We'll need to find another fundamental improvement in lens technology to shrink the next 50%
I'd say the biggest unsolved issue is the focus/depth of field issue...how to provide variable per pixel depth so that virtual objects can appear in a scene and be focussed on naturally (apparently called vergence–accommodation conflict) since most if not all displays have a fixed focus distance atm.