Life Path and Personality Conflict

I'm uncertain what you mean by conflict. If you are referring to compatibility, the energy represented by your life path number, the number 9, is somewhat compatible, not incompatible, with your personality and your soul urge/heart's desire numbers, both the number 5.

The numbers aren't the same, but they are compatible. As is the energy of your destiny number, the number 1.

There is a compatibility chart at the Compatible and Incompatible Numbers page.

If there was incompatibility, it generally would tend to bring events and circumstances for a full and deeply experienced life. But other incompatibilities can provide that (most numerology charts do), so a person doesn't end up with a shallow life.