  We compute the space of 5x5 matrices of tropical rank at most 3 and show that
it coincides with the space of 5x5 matrices of Kapranov rank at most 3, that
is, the space of five labeled coplanar points in TP4. We then prove that the
Kapranov rank of every 5xn matrix equals its tropical rank; equivalently, that
the 4x4 minors of a 5xn matrix of variables form a tropical basis. This answers
a question asked by Develin, Santos, and Sturmfels.
