Because it wasn't spell it with a
E to A is a fourth of some type. Lower the
E with a flat and it becomes an augmented fourth. Add the sharp to the
A and it is augmented (made larger by a half step) again and so it's called double augmented, a double augmented fourth.
...Is it simply because the enharmonic equivalent Bb should have been used, as that’s in the Eb scale?
Which is it?
Yes, they are enharmonically equal, but the whole point of asking about
A# is to see if someone understands complex interval spelling in writting notation.
...I counted up 7 semitones...if played you’d identify it as a perfect fifth...
That's beside the point. The interval was spelled out with sharps and flats.
We need to take a step back and think about terminology.
Interval in the generic sense is just a distance of time or space, or some other measurable thing. If there are 7 steps between two things, it's just an interval of 7. (Not a musical seventh, I mean the distance is just 7 units, frets, piano keys, etc.) If the two things were frequencies you could describe the interval with a ratio like 3:2.
But, those are merely "physical" measurements. They are not musical notation.
7 half steps or 3:2 is not a perfect fifth. They are possibly a perfect fifth, double augmented fourth, diminished sixth, etc. You cannot use terms like perfect, augmented, diminished, etc. until the interval is notated or spelled with the letters and sharps and flats of notation.)
If someone played the two tones would they identify a perfect fifth? Yes. But that would be a kind of ear training test.
The question as asked is a test of notation reading.