The 7#5 Chord

C7#5 would be spelled.. C E G# Bb
and would resolve to a F or B chord.

The 7#5 chord gives you a stronger sense of drama and urgency than a
plain dom7 chord. The chord still resolves down the same as a dom7:
down by a P5 or half step (tritone sub)

In the dom7 to I chord progression (ex. G7 to Cmaj) the b7 resolves
down a half step to the third of the I chord. In the 7#5, the #5 resolves
UP a half step to the third. (ex G7#5 to Cmaj - the note D# resolves up a half step
to E. So you have another chromatic approach to the third of the I chord.

Remember once you sharp the "5" (fifth scale degree), you can no longer
play the regular fifth scale degree or it will clash. It is no longer "legal"
in the traditional sense.