Welcome to the forums!
First, let's make sure your press grip is correct. Please review the two links below:
Gripping Matters | Jordan Feigenbaum
Mark Rippetoe: Press Grip - YouTube
Pressing and bench pressing while squeezing the crap out of the bar, with a correct grip, will build requisite grip as part of the whole system. So will deadlifting with a double overhand grip. Just curious, what are you deadlifting for a set of 5? How do you grip it?
As far as the power clean goes, I would like to see how you rack the bar. Assuming you let it roll into your finger tips like it should, your grip may be too narrow. It's hard to say though, I can't see you from here!