What is the phase shift of y=(5/3)cos(4x-pi)+4

$$\\y=(5/3)cos(4x-pi)+4\\\\ y=(5/3)cos[4(x-\frac{pi}{4})]+4$$

Phase shift is pi/4 to the right

This old post goes into more detail

http://web2.0calc.com/questions/graphing-trig-functions_1#rr2

We can write

y=(5/3)cos[4(x-pi/4)]+4

This is the cosine graph with an amplitude of (5/3) shifted up 4 units

There are 4 periods in 2pi

The phase shift is pi/4 units to the right........