The fourth requires probable cause. The law enforcement people must believe Cohen's actions meet the standard.
There are provisions in statute involving the suspicion of criminal actions by which the AG can set aside the privilege between an attorney and their client.
Rosenstein must have signed off on the raid.
csl, you continue to see absolutes in the bill of rights. But rights conflict. The fourth amendment was mostly designed in the English common law (check Edward Coke) and was created specifically in the way the common law treats problems: there are principles and there are exceptions to principles.
Probable cause, the American slice of the fourth amendment, means that a judgement is made between the rights of the suspect and the interests of the law.
So basically, you may reasonably conclude that they (including Rosenstein) have strong presumptive evidence that Cohen is a crook. And the raid was undertaken because the law required it.
On the fifth - well, I am shocked to hear that you think the president has engaged in the sort of criminal behaviour to which the fifth amendment applies. But if you think he requires the protections of the fifth amendment, I assume you also believe he ought not to be president as a criminal is not presidential material and a criminal's secret actions leave them vulnerable to extortion by a foreign power.