I read that when you take away the fifth in a seventh chord it's still considered a seventh chord. But how would you differentiate between a seventh chord with a fifth and without one? Like is there a Gmaj7Without5 or some other notation?
It's very common in guitar chord voicings to omit the fifth without any specific marking for it, these are called "shell chords" (https://www.jazzguitarlessons.net/blog/shell-voicings-jazz-guitar)
The fifth isn't a "guide tone," like the root or 3 or 7 which determines the quality of the chord (happy/sad/dominant/dissonant). It's a perfect interval, emotionally neutral and functionally just amplifying the main harmonics of the root. When you leave out the 5, the chord sounds less crowded and you can hear more of those guide tones that strengthen the harmonies.
But as the other answer mentions, the "no5" notation is sometimes used to be extra specific.
I've seen formatting like Gma7(no5) in guitar tabs. No idea if its standard or used in other contexts.