Now apply the Kirchhoff's voltage (loop) rule.
Loop I (going around clockwise) includes the battery V, R1 and R4. The corresponding equation is:
V=R1 I1 + R4 (I1 - I3 ).
Loop II (going around clockwise) includes R1, R2 and R3. The corresponding equation is:
R1 I1 + R3I3 = R2 I2 .
Loop III (going around clockwise) includes R4, R3 and R5. The corresponding equation is:
R4(I1-I3)= R3I3 + R5 (I2+I3 ).