Signal flow simplification
There are a few rules you need to know in order to simplify this,


Branch Move Rule:




and Negative feedback Rule, which says that a system of the form shown below



has transfer function

$$
T = \frac{Y}{X} = \frac{a}{1 + ab}
$$

To solve your problem you have to move the X2 node to the right across G2 then move the X3 node to the left across G2.After that you then use the Negative feedback rule to get the transfer functions of different portions of the signal flow diagram then multiply them out to get your final transfer function.

You should get something along the lines of

$$
T = \frac{X_4}{X_1} = G_2 \frac{G1}{1 + G_1G_2G_3} \frac{G3}{1 + \frac{G_3G_5}{G_2}} 
$$