While some doubt has been cast on whether a fair trial was actually conducted here and although my jurisprudence is a bit rusty, I think it's quite safe to assume from the problem given that all five were indeed duly found to be ˜guilty as charged".  Here's my spin!

Initially, we know Mr. Murder didn't do it, and by his different sentence, Mr. Theft didn't do it either, leaving only Messrs. Fraud, Libel and Blackmail as possible candidates.

Assume Mr. Fraud (namesake of fraud) actually committed the murder.  By applying para. 4, it's quickly apparent that the fraud charge itself then went to Mr. Murder (namesake of murder).  Kind of simplistic, but things work neatly that way!  But if Mr. Murder was charged with fraud and Mr. Fraud was charged with murder, para. 3 results in Mr. Blackmail's crime being murder as well, which is a contradiction.  So, Mr. Fraud couldn't have done it!

Let's assume Mr. Blackmail did it.  From para. 3 again, the namesake of his crime would of course be Mr. Murder, who would then have been charged with the namesake crime of the murderer, blackmail!  But working that result through para. 4 to its conclusion, however, Mr. Murder would then have also been charged with fraud.  Another contradiction, so Mr. Blackmail's out too!

That only leaves Mr. Libel as the murderer, as others have already determined.  Moving on, since the namesake of Mr. Blackmail's crime (from para. 3) is charged with libel, the only two remaining charges possible for Mr. Blackmail are now just theft or fraud. 

Assume Mr. Blackmail was charged with theft.  Following from para. 3, Mr. Theft therefore had the libel charge.  By elimination to this point, that leaves only the blackmail charge for Mr. Fraud and the fraud charge for Mr. Murder.  This would be contrary to para. 4 which would conclude that Mr. Blackmail, and not Mr. Murder, had the fraud charge. 

So Mr. Blackmail had the fraud charge, and as per para. 3, Mr. Fraud then gets the libel charge.  By elimination again, Mr. Theft is left with only blackmail, and therefore Mr. Murder got the theft charge.  All of which satisfy the problem nicely.