One approach with lex-sorting -
# Perform lex sort and get sorted data
sorted_idx = np.lexsort(data.T)
sorted_data =  data[sorted_idx,:]
# Get unique row mask
row_mask = np.append([True],np.any(np.diff(sorted_data,axis=0),1))
# Get unique rows
out = sorted_data[row_mask]
Sample run -
In [199]: data
Out[199]: 
array([[1, 8, 3, 3, 4],
       [1, 8, 9, 9, 4],
       [1, 8, 3, 3, 4],
       [1, 8, 3, 3, 4],
       [1, 8, 0, 3, 4],
       [1, 8, 9, 9, 4]])
In [200]: sorted_idx = np.lexsort(data.T)
     ...: sorted_data =  data[sorted_idx,:]
     ...: row_mask = np.append([True],np.any(np.diff(sorted_data,axis=0),1))
     ...: out = sorted_data[row_mask]
     ...: 
In [201]: out
Out[201]: 
array([[1, 8, 0, 3, 4],
       [1, 8, 3, 3, 4],
       [1, 8, 9, 9, 4]])
Runtime tests -
This section times all approaches proposed in the solutions presented thus far.
In [34]: data = np.random.randint(0,10,(10000,10))
In [35]: def tuple_based(data):
    ...:     new_array = [tuple(row) for row in data]
    ...:     return np.unique(new_array)
    ...: 
    ...: def lexsort_based(data):                 
    ...:     sorted_data =  data[np.lexsort(data.T),:]
    ...:     row_mask = np.append([True],np.any(np.diff(sorted_data,axis=0),1))
    ...:     return sorted_data[row_mask]
    ...: 
    ...: def unique_based(a):
    ...:     a = np.ascontiguousarray(a)
    ...:     unique_a = np.unique(a.view([('', a.dtype)]*a.shape[1]))
    ...:     return unique_a.view(a.dtype).reshape((unique_a.shape[0], a.shape[1]))
    ...: 
In [36]: %timeit tuple_based(data)
10 loops, best of 3: 63.1 ms per loop
In [37]: %timeit lexsort_based(data)
100 loops, best of 3: 8.92 ms per loop
In [38]: %timeit unique_based(data)
10 loops, best of 3: 29.1 ms per loop