Possibly another opportunity to make a fool of myself. Please pardon me in advance if that is a silly question.
I have a nice uAvionix AV-30, which computes (among others) the True Air Speed. As far as I can tell, the TAS calculation of the AV-30 is correct (per the web calculator here)
In my understanding, Ground Speed corresponds to TAS + wind effects. However I realized (many times) that my ground speed is usually IAS + wind, not TAS + wind. On days without wind, IAS as reported by the AV-30 is even within 1kt of GS. Right on the money.
What did I get wrong?
How did you measure your ground speed?
When you correct IAS for position error you get CAS which you correct for compression to get EAS which you correct for density to get TAS. GS is TAS corrected for wind.
Well, the best definition is: The true airspeed (TAS; also KTAS, for knots true airspeed) of an aircraft is the speed of the aircraft relative to the air mass through which it is flying.
You are not the only EuroGA user having problems grasping the concept of those different speeds, but help is at hand 
There is plenty of online stuff written by well qualified pilots, and those will hopefully clear your assumptions… one good example in Understanding True Airspeed
But in a nutshell:
Forget CAS for the moment.
To convert IAS to TAS, add 1.5% to 2% per 1000ft. So at 5000ft, an IAS of 100kt will be a TAS of about 107-110kt. If whatever instrument you have is telling you otherwise, it is probably dud – unless the temperature is way off standard. There are TAS calculators online where temperature can be entered, and there are slide rules which do it.
Another way to get a dud TAS is if the OAT is wrongly measured. Any decent TAS display will use IAS, pressure altitude, and OAT. This was classically called an “air data computer”.
GS is easy: straight off the GPS.
GS is indeed TAS +/- wind but only if there is no crosswind component.
Something is wrong somewhere…
IAS to CAS correction should not be big when in level cruise. A standard pitot and a standard ASI should read pretty well right.
An ELI5 explanation could be that
the small opening of the pitot tube just can’t accurately make use of the air (= can’t read the real, true air speed) anymore the higher and faster you go. Mach speed comes to the rescue. The airplane’s wings suffer the same fate, hence aerodynamically IAS remains relevant.
Compare CAS here to TAS & EAS, e.g. at sealevel (almost no difference) vs 10.000 ft. (significant difference).
To still give you a reading of (air) distance covered in time, the (for this purpose) “erroneous” IAS is corrected (in steps of CAS and EAS) to give you TRUE Air Speed. To give you distance in time over the ground, TAS is corrected for wind, giving you GS.
This is easier in a balloon 
What is ELI5?
One never calculates GS. One just reads it off the GPS.
See also ASI calibration for background.
I suspect the AV30 is duff or something isn’t connected.
Dan, “Help is at hand… There is plenty of online stuff written by well qualified pilots…”
That webpage is an excellent example of pilots who pretend to understand airspeeds.
Snoopy, “ Mach speed comes to the rescue.”
I hope not!
IAS is what makes the aircraft fly. GS shows how fast you move across the earth. TAS is mostly irrelevant, but used to be important when the slide ruler was popular.
