Step 1: According to (1), the chemistry teacher and the math teacher live together; (5) The oldest of the three teachers lives farther than the other two; It is known that teacher B does not teach chemistry and mathematics;

According to the fact that the physics teacher is older than the biology teacher and younger than the B teacher, it is concluded that the B teacher is the oldest, followed by the physics teacher and the youngest. Teacher A is a biology teacher because she is the youngest. This shows that Teacher B doesn't teach biology and physics.

Conclusion: Teacher B teaches Chinese and history;

Step 2: According to (3) math teacher and C love playing chess; (1) The chemistry teacher and the math teacher live together; It can be known that chemistry is taught by C;

According to (2) Teacher A is the youngest (4) The physics teacher is older than the biology teacher and younger than Teacher B; You can know: c teaches physics;

Conclusion: Chemistry and physics are taught by C;

Step 3: The rest study math and biology.