I think you need to clarify if the connector is male or female as well as specifying if you are looking at the external connection side or the internal soldering side.

To encourage one standard, The MIDI Association specification for the TRS connectors uses the pin assignment that is called Type A. The pictures in the spec show a female connector and looking at the external connection side. I especially like the picture of the cable itself on page 2, that makes it a little more obvious what the diagram is showing.

Just for completeness, an image (front/external side for female/socket; solder/internal side for male/plug).

Thanks guys.  In truth the reality of wiring it up via just the logic of how things are connected is not a problem at all.  I know how the MIDI Out socket will have its Sink and Source lines connected so I could just assume that and follow it through.  I have the MMA Letter of Agreement of the standards already to refer to as well.  The issue my brain can't get around is that my cable plugs (male) seem to have incorrect numbering.

I tried to describe the orientation but I guess it is difficult to make it clear in just words.  Here is a link to the picture on my Dropbox site:  5pin DIN numbering  You can see from that pic that the socket numbering in the upper half drawing with the TRS jack seems to match what I am seeing elsewhere.  That is looking into the insertion face with the solder buckets into the screen.  The lower half is of my own plug viewed into the mating pins, i.e. from the insertion side with the solder buckets away from us into the screen.  That is numbered exactly the same!  My brain tells me it should be reversed to match the socket when it is inserted.  There are many other sites I looked at which show the same contradiction with my plug.  For example Philip Rees has a simple guide to wiring up a MIDI plug which is very clear.  It also contradicts my own plug numbers.

I could ignore this and just start at the MIDI Out socket and follow the logic but, not being a MIDI guru, I was worried I might be missing some peculiarity of the system and end up wiring it the wrong way round because of that.  As long as my plug is numbered either incorrectly or perhaps even to some different standard (???) there is no problem.  It's just confirmation that I can ignore that plug numbering and continue using what God gave me upstairs that I would appreciate.

These numbers indeed are wrong for a male plug.

Does this thing have a name and/or a datasheet?

Thanks for confirming that Clemens.  Yes, it is blatantly incorrect according to most info out there.  However, what I have found is that everyone knows how MIDI should be wired up but there is much confusion caused with pictures posted showing it where it is not made absolutely clear which way plugs and sockets are being viewed.  I have found pictures where a cable is being defined but the DIN connection at one end is apparently the wiring of the socket in the unit and not the plug on the end.  I do find such inconsistencies very frustrating as someone who always attempts to clarify things to the point of irritation for others, (I mean I can be a pedant).

I've taken the pragmatic view and used the existing basic info for the wiring of the MIDI Out socket I'm attaching the cable to, and simply worked from there to the TRS jack ignoring any plug numbering completely.  Assuming the MIDI Out socket is viewed from outside the Master unit looking into its mating face, and with the pins to the bottom, (smiley face orientation), Pin 4 will be to the right and pin 5 to the left of pin 2 in the centre.  I have wired pin 4-Source to the Ring and pin 5-Sink to the Tip of the TRS jack.  This should conform with Type-A standard - unless anyone tells me different, (I can always be wrong of course)!

I'll now have to take the cable to where it can be tested with a live unit over the next day or two, this isn't for my own use, and I will be sure to confirm whether this is correct or wrong after that.

I'm not sure what you meant when you asked for a name or datasheet.  In terms of the units involved, the master unit is a Boss RC-202 Loop Station also controlling a Boss RE-202 Space Echo pedal.  The RC-202 has standard DIN5 MIDI Out and the RE-202 has a Type-A 3.5mm TRS MIDI In according to their specs.

The cable is a generic MIDI Din5-Din5 bought from a reputable supplier as it has a good quality thick braided cable type which is good for rougher onstage treatment.  The original connections as supplied have been made cleanly and with decent soldering technique.  I have removed one of the DIN plugs and am fitting a Rean made 3.5mm TRS plug with a larger cable entry to suit the thicker cable type.  (I always stick to Neutrik/Rean wherever I can as I have always found them to be top notch connectors at a sensible price.)  There should be nothing unusual about that.  The DIN-5 plugs supplied are again decent quality - except for this anomaly of their numbering.  I have contacted the supplier pointing this out.

I meant the cable. Apparently, that reputable supplier did not use a cable assembly from a reputable supplier.