I took another look at Boss 4, and the reason why I struggled so much is two-fold.
First, Boss 4 has a three-to-four hit combo where the last hit is unblockable, requiring an attack parry rather than a regular parry. But the thing is, there is very little room to figure out how many swings he is going to use, while Boss 5 will always use two axe swings before an unblockable attack.
In addition, Boss 5 has visual feedback when you successfully parry his third axe swing, while the feedback for parrying Boss 4's attack is present but far more subtle.