Although your question seems like a legitimate inquiry, it's also possible that it is a trick question. Let me take each idea in turn, and then you can decide.
First, let's take the question at its word. It is asking what Charis "triumphs over" in lines 5-9. First, let's examine the exact text of those lines:
As she goes, all hearts do duty
Unto her beauty;
And enamour'd, do wish, so they might
But enjoy such a sight,
That they still were to run by her side,
It is important to realize, first, that although "Charis" is only used in the title, it is one of the Greek words for love. (I, as well as other scholars, have also entertained the idea that Charis could be the actual name of the woman who is loved in the poem.) Keep in mind that the poem speaks of "the chariot ... of Love" that holds "my lady." It is this lady that many say is the "Charis" who here triumphs over "all hearts." Why? Because "all hearts do duty" to her. They also all wish to "enjoy such a sight" as to "run by [the] side" of "my lady."
However, I must also say that these are odd lines to choose to answer this question. Why? Because in my opinion, I would use the following lines as my primary support:
As alone there triumphs to the life
All the gain, all the good, of the elements' strife.
In other words, strife has no meaning because Love allows the lover to see "all the gain" as well as "all the good." So this is a true triumph of Love over the "strife" of "life." Also note, however, that the words "triumphs over" are never found in the poem! This leads me directly in to the next idea.
It is possible that this is a trick question. The word "triumph" is a pickle in itself because it might not mean to "triumph over" anything... instead it could mean a simple celebratory procession! In fact, it's truly possible that the latter is the case! If you want to consider this scholarly idea, then this is a trick question and, in fact, those exact lines of 5-9 are the reaction of the people (especial males) tracking this procession.
Another two interesting ideas relate to the next two stanzas. The second stanza is a description of "my lady" in the chariot of Love. The third stanza is mostly a series of questions about beauties of the earth that further "my lady's" description. Because of the percentage of the poem this description encompasses, it's possible that it is Love's procession being described instead of Love's triumph "over" something.
If pressed, and if we are still assuming this might be a trick question, I guess we could go back to the old adage that "love conquers all," but that is a stretch. Why? Because there isn't really a description of anything that is truly "triumphed over" here... unless you count the brief mention of "strife."