Conditional Formats will only do that - format. I presume that your first conditional format sets the font colour to white or similar.
What you could do is to move the present calculation of C1 to another cell - say Z1. Then in C1 use the formula
=IF(Z1=<5/24, Z1, Z1-0.5/24)
and make sure Z1 and C1 are formatted as time.