If the piano is tuned properly, by a trained professional, then all the notes will be equally "in tune" and all the 5th will be identical. It goes without saying that this doesn't apply if you have a bad piano tuner.

But there is no such thing as one single equal temperament. There are many different permutations.

12-TET is favoured by some tuners, but the results can be quite unsuccessful with thirds (see above)

*There is some more information about 12-TET, and the reasons & places it goes wrong on pianos, here on WikiPedia. Some of this stuff is specific to pianos and their mechanisms. There is a detailed listing of the mathematically 'correct' frequencies of all 88 notes of a concert grand, but in reality - explanation given there too - these are not always the best choice. So when you ask for 12-TET, in 95% of cases you're still not getting it, but the tuner's corrected version of it instead.*31-TET is used by many professional tuners these days. It tempers the fifths, in order to get the thirds in closer.

There is also 41-TET, which is a decent compromise, but there are still some ropey fifths. The tuners at the Moscow Conservatoire use 41-TET, unless given other instructions, for example. 53-TET is the closest usual tuning to strict Pythagorean, but it drives people bonkers. It's used in Turkish music, though.

Some performers of atonal music go for 72-TET, which is a correcter "mathematical" squeezing. But I don't know any tuners who will put this tuning onto an instrument that is intended for general use - and in fact many would baulk at it entirely.

It's worth remembering that 'just temperament' is not the same as 'equal temperament'.

** It's also worth remembering that the words 'temper' and 'tamper' have the same root **