A numpy array with shape (5,) is a 1 dimensional array while one with shape (5,1) is a 2 dimensional array. The difference is subtle, but can alter some computations in a major way. One has to be specially careful since these changes can be bull-dozes over by operations which flatten all dimensions, like np.mean or np.sum.
In addition to @m-massias's answer, consider the following as an example:
17:00:25 [2]: import numpy as np
17:00:31 [3]: a = np.array([1,2])
17:00:34 [4]: b = np.array([[1,2], [3,4]])
17:00:45 [6]: b * a
Out[6]:
array([[1, 4],
[3, 8]])
17:00:50 [7]: b * a[:,None] # Different result!
Out[7]:
array([[1, 2],
[6, 8]])
a has shape (2,) and it is broadcast over the second dimension. So the result you get is that each row (the first dimension) is multiplied by the vector:
17:02:44 [10]: b * np.array([[1, 2], [1, 2]])
Out[10]:
array([[1, 4],
[3, 8]])
On the other hand, a[:,None] has the shape (2,1) and so the orientation of the vector is known to be a column. Hence, the result you get is from the following operation (where each column is multiplied by a):
17:03:39 [11]: b * np.array([[1, 1], [2, 2]])
Out[11]:
array([[1, 2],
[6, 8]])
I hope that sheds some light on how the two arrays will behave differently.