Image.transform(size, method, data) with method=Image.AFFINE returns a copy of an image where an affine transformation matrix (given as 6-tuple (a, b, c, d, e, f)via data) has been applied. For each pixel (x, y), the output will be calculated as (ax+by+c, dx+ey+f). So if you want to apply a translation, you only have to look at the c and f values of your matrix.
from PIL import Image
img = Image.new('RGB', (100, 100), 'red')
a = 1
b = 0
c = 0 #left/right (i.e. 5/-5)
d = 0
e = 1
f = 0 #up/down (i.e. 5/-5)
img = img.transform(img.size, Image.AFFINE, (a, b, c, d, e, f))
img.save('image.png')
