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.
If I'm looking strictly from a jazz perspective, the above conversation seems right. However, once I get into pop / electronica / EDM...I'm working with sequencers, and there it makes a big difference whether you're holding down the key for the fifth of a chord or not.
That said, standard music notation only covers 90% of what I've needed. I've had to invent a lot of notation, especially when it comes to what scale to play over a passage (e.g. using G" to denote a G double-soul ionian scale). I worried about being needlessly innovative until I learned the history of music notation, and then realized everyone from 14th C monks to 20th C jazz cats were making it up as they went. Innovating missing notation is part of the equation.
I use D7 x5 for "D7 no 5th"? Months later, when I look at my scores, I still know what I meant. When I writing for my band, I put a "notation legend" at the bottom to explain whatever I use. Everyone seems to do well with it.
I personally have never seen a (no5) notation in any official charts in the last 50 years. I am not sure it's a new convention or just one I've missed. Or perhaps we don't use it on this side of the pond. In classical 4 voice homophonic harmony theory the 5 is considered optional. Depending on how the other notes are moving you can choose to use it or not, if not you usually double the 1 (with its octave). In guitar charts I've never seen it notated but have been taught to "grab what works" in the moment.