Why would you expect there exists built-in code to do something totally unusual like this? Built-in code is written to solve common problems. It should be something that a wide variety of users will find valuable.
You have scattered data in 3-d. The problem is, this is an optimiztion problem, but it is significanty a piecewise constant thing. That is, your objective is to maximize the count of points inside the cube. But you will be able to shift the cube by some amount in any direction (most of the time) and not change the number of elements in the cube. So your objective is a piecewise constant thing, a highly nasty thing to try to optimize. Don't even think of trying to use a general optimizer like fminsearch or fmincon/fminunc.
How would I solve it? I would discretize the problem. Create a 3-d array, where the indices are a scaled, discretized version of (x,y,z). Each element of the array is then the number of points that fell within 5 units in any direction. Do this all by a simple loop, where you increment by 1 all cells in the array in the vicinity of each point. (This can be done quite efficiiently. Learn about sub2ind, and how dfata is stored in an array in MATLAB.)
When done, just find the cell of that array that has the maximum count.
