Place four of the eggs in a medium pan, cover with water and bring to the boil. Simmer for 7mins. Drain the eggs, then rinse in cold water. Tap the shells all over and peel away. Roughly chop the eggs.
Place the potato and vegetables in a large bowl with the chopped eggs and seasoning. Beat the remaining egg, add to the potatoes and mix well. Divide and shape the mixture into 8 small or 4 large cakes, dusting them lightly with flour as you go.
Heat the oil in a large non-stick frying pan, add the cakes and cook for 8-10mins turning over half way through until they are golden brown on both sides. Lift from the pan with a spatula, draining on kitchen paper then serve hot.