A fifth in 12-TET is defined as seven semitones. Instead of multiplying your frequency by 3/2, you multiply by the 12th root of two seven times, which is about 1.498. That’s close, but not quite on the nose. Major thirds are worse in 12-TET. Instead of multiplying your frequency by 5/4, you multiply by the 12th root of two four times. That gives you 1.25992, which is not very close to 5/4 at all. Nevertheless, we as a civilization have collectively decided that we should just suck it up and live with everything sounding a little wrong. There are plenty of good reasons to!
Whether you’re recording yourself or someone else, you’ll save time in the long run by getting lots and lots of takes. The most obvious reason for this is that musicians typically need a couple of run-throughs to start feeling comfortable and confident. But you also need to give yourself as many options as possible for splicing things together during the editing process, so you don’t have to go back in and record “punch-ins.” Re-recording is a time-waster; recording songs more than once the first time is a life-saver.