Based on the specs in your post I’ve calculated the cable voltage drop using http://www.calculator.net/voltage-drop-calculator.html
Voltage drop: 7.94V
Voltage drop percentage: 66.17%
Voltage at the end: 4.06V
This is calculated with the full load of 25A going through the cable, so with a lower load you would get a higher voltage.
Real world conditions may be different.
I would suggest using a shorter cable with thicker conductors. A big electrolytic capacitor or a super capacitor at the ROV end would help to buffer this voltage too.