My claim took two years to get to the point where court action was threatened. It is usually only a threat though and very few cases go all the way to court. Usually the insurance company gets the summons and pays up (so I was told).
5 months is also quite usual for the medical examination, as the solicitors will want to wait till all symptoms have become apparent. The examination is in essence you telling someone all the symptoms you had, the time it took for them to go away etc. The dr basically sits there and takes notes and then makes a report for both sides (and the court if it go that far). As its a long time ago, you can probably labour the pain and trauma stuff as no one can prove otherwise and the examiner will just put it in his report.
All elements of my claim were bundled together in the same settlement BUT stuff like the damaged bike was paid out early in the process as it was tangible. You should have had some money for the bike by now I would have thought. Edit. just realised that no responsibility has been accepted so this is probably why no payments have been made yet.