C7(#5) Chord on Guitar

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7(#5) is just an alternative notation for a 7(b13) chord. 7(b13) is the recommended notation.

[1]7(#5) has the notes [1] (1), [3] (3), [#5] (#5) and [7] (7).
[1]7(b13) has the notes [1] (1), [3] (3), [b13] (b13) and [7] (7).
[b13] and [#5] are so called enharmonic equivalents and therefore sound the same.

Please also read the description of the [1]7(b13) chord for informations how this accord can be practically applied.

Here is why I would prefer to notate this chord as [1]7(b13) instead of [1]7(#5):
Every chord relates to one or several scales that can be used to write melodies or improvise over that chord. In case of [1]7(b13) respectively [1]7(#5) chord the most common/prefered scales are:
[1] HM5 (Harmonic Minor 5):
[1] (1) [b9] (b9) [3] (3) [4] (11) [5] (5) [b13] (b13) [7] (7),
[1] Altered Scale:
[1] (1) [b9] (b9) [#9] (#9) [3] (3) [#11] (#11) [b13] (b13) [7] (7),
[1] Whole Tone Scale:
[1] (1) [9] (9) [3] (3) [#11] (#11) [b13] (b13) [7] (7)

7(b13) leads to the assumption that the relating scale can have a perfect 5th (5) or a b5/#11 (that is right!), while 7(#5) might lead to the wrong assumption that the scale might also contain a perfect 6th/13th, which would result in a scale with two consecutive half steps: #5-13-7.

You may want to argue that some books/resources also write the mentioned scales with a #5 instead a b13, but this for me destroys the concept of natural tensions 9-11-13 versus altered tensions b9/#9-#11-b13.

Another important point that speaks for 7(b13): it is great for fast and accurate reading, if certain intervals only come up with certain chord types:
b5 is most likely associated with a diminished or half-diminished chords and therefore a minor 3rd
#5 is usually associated with and augmented or maj7(#5) chord, which both have a major 3rd in it,
#11 and b13 is normally associated with a dominant 7th chord.

I heard somebody saying that for him 7(#5) means that the #5 is obligatory while b13 means you may add a b13 by choice. That makes no sense for me. There is no parameter in chord symbols that determines a level of obligation or voluntariness. Your musical freedom is much more determined by musical style, instrumentation, arrangement and your personal level and experience.