I am in favour of fixed term parliaments.
The current system is basically undemocratic, in my view. It is manipulated by the party in power, to hold an election whenever they think that they are most popular, in order to stay in power and hopefully win a bigger majority. Generally, governments hold an election after four years, if they are popular, but hang on till the end of a five-year term (the maximum length of a Parliament) if they are unpopular - thus prolonging in power what is often a deeply unpopular government.
Fixed term parliaments would remove this power to manipulate election times to party advantage. They would also benefit the economy, since businesses would be able to plan for when there would be an election and a potential change of government; at the moment, this is not possible.
There is a legitimate concern that 5 years is too long. 4 years would be line with the length of administrations in the USA. Perhaps we could even synchronise our elections with US presidential elections, so that there is the same team in the White House and the same team in No 10, over the four-year period.