2Donkeys - I agree with you on this one as it is a constant source of discussion within the Training world.
I read the pilot in 5.a as being the person being trained/examined/assessed for licence issue/renewal. He/she is authorised by Para 5.a to pilot (handle) the aircraft even though they may not have an appropriate licence to do that. Note, it does not matter if they already hold, say, a PPL and it is simply being renewed or extended, as most basic training aircraft are single crew anyway. They are therefore handling the aircraft while the Single Crew pilot (ie the PIC Instructor) sits and Instructs/assesses. One of the conditions of them being allowed to pilot Single Crew aircraft even though they are not PIC is that no other person may be carried in the aircraft (Para 5.b.i) unless they have a formal part to play in the proceedings as defined in the exceptions to Para 5.b.i.
Note that it is not a case of who is PIC. It simply states that the trainee/assessee is not permitted to pilot the aircraft if another person is sat in the back. The only exception to this is where the person in the back is also undergoing training and will benefit from the experience (5.b.i.cc). For example, one student flies one leg and then the other student flies the next leg. Watching from the back is excellent training and satisfies 5.b.i.cc. But the students need to be of a similar stage in their training to benefit and you would have to prove that through Student Records or similar documentation. The Trial Lesson (Lesson 3 in the PPL course) case is no exception to 5.b.i.cc and is one where I believe you can carry an "observer" as they are at a similar level. I brief student and observer together and ask them both if they have any questions before we walk out to the aircraft. On one occasion the "observer" came back for more but the "student" decided to stick to fishing or whatever he was in to!!!!
Finally, I would not carry someone in the back unless I could prove 5.b.i.cc as most Insurance is linked to the aircraft being operated legally. Given the dreadful situation where an accident arises the Insurance company would look very closely at who was doing what and why, and you would need to prove to them that Aunt Maud, who was sat in the back at the time, was actually training and not just enjoying the view.
Noggin - just a small point but a Trial Lesson is an official lesson - also called an Introductory Flight or Air Experience Flight! Lesson 3 if I'm not mistaken - not got a Syllabus to hand! It is just as valid as a "Stalling Lesson" or "PFL Lesson".
Fly-by-Wireless - The rules on your question are clear - no matter how "skint" you are! If you fly and don't cover your portion of the cost you are gaining free hours. The rule is cost-sharing. You can split the cost of the flight between all the occupants but you MUST pay your share! As an aside, your use of the phrase "show-off flight" is a worry to me as an Instructor. "Showing off" kills people pure and simple. I know what you mean but the phrase "show-off" sends a chill down my spine. Sadly, I personally know at least one person who died - probably "showing off" knowing the person/circumstances. Picky I know but attitude is all important in flying. Anyway, good luck with your Training!!!!!!
Regards, H 'n' H
PS Willing to stand to be corrected as, is ever the way in aviation, things are often far from clear!