If you want the conviction taken off your CCAP record that is done through a petition to the court. If you want it completely off your record you would have to seek a pardon from the Governor, and as that sounds, it's not easy at all. It may be best to start with expunging it from CCAP as that may increase your odds in employment since some employers don't do the highest background checks and simply check CCAP but you'd have to be honest on applications about convictions.
Unfortunately, there isn't any way to expunge your 2005 Class H felony conviction. Though the expungement statute (973.015) allows for certain H felonies to be expunged now if you're 25 or under and have no prior felonies when convicted, that change occurred in 2009 and only applies to convictions that occurred after the change. it is possible, depending upon what county your conviction occurred in and how kind the charging DA is feeling, that you could ask to have the case reopened for sentencing and have them amend it down and/or dismiss it (though I wouldn't try it without hiring a lawyer to help you, because it's not the easiest thing in the world to do.) However, not to be a pessimist, but seeing as how this question is coming from Waukesha, if this happened in Waukesha County I can guarantee you that none of the judges there would even remotely consider doing this for you.
I'm sorry if this answer isn't what you wanted to hear!
Difficult but worth a shot.
I would contact DA and see if there was any possibility of reopening case, esp. if no priors.
Was there a prior criminal record?
Does 973.015 Special disposition apply?