5:2 fasting is a less harsh development of Alternate Day Fasting which is in turn a relaxation of a severe fasting diet called Calorie Restriction, about 600 cals per day. The primary objective of CR is not weight loss but to increase longevity by slowing the ageing process and reducing the possibility of developing various cancers.
The evidence for Calorie Restriction is better than for Alternate Day Fasting.
Alternate-day fasting and chronic disease prevention: a review of human and animal trials
Evidence for increased longevity with the 5:2 diet is even less clear. However interest in weight loss was sparked when it was discovered that on non fasting days, people only ate 125% of their normal intake. It had been assumed that they may eat much more after a fast day. Overall, they eat less in a week on this diet.
Take for example someone who eats 2400 cals per day, ie 16,800 cals per week. On the 5:2 diet they should eat 1200 cals for the two 'fasting days', ie 600 per day and 2 days at 3000 cals per day, ie 6000 cals and 3 normal days at 2400 cals, ie 7200. The total intake is therefore 14,400 cals, a net saving of 2400 in one week. Hence, if weight is stable at 2400 cals per day, on the 5:2 diet you are likley to lose weight slowly, about as much as someone who dropped down to 2000 cals per day on a normal diet, 1/2 lb to 1 lb per week.
People I know who have tried this appear to lose weight at this rate so as a long term thing, it is OK for a healthy person. It's not the quick diet for someone who wants to look good on the beach in a couple of months time though. It is just a trade between speed of weight loss and severity of the diet. Many people find a traditional 1200 cals per day type diet too severe or impossible if they have to utilise ready meals or eat lunches at work, usually via the sandwich shop. The soup, sandwich and bun already takes up a sizeable proportion of that 1200 cals.