Why do we have 5 days working in a week?

It was supposed to be a 6 working days week and then an off. The day off depends on the particular region's culture and religious practices in that geographical arena. Friday for Muslims, Saturday for Jews and Sunday for Christians is being followed now.

It all has changed after that US big companies first started giving holiday on Saturday for their Jewish employees for Sabbath and Sunday for their Christian employees. It has slowly transformed into 2 days of holidays from work in a week. Gradually even other companies also started giving Saturday as a holiday. 

According to Wikipedia:

"In 1926 Henry Ford began shutting down his automotive factories for all of Saturday and Sunday. In 1929, the Amalgamated Clothing Workers of America Union was the first union to demand a five-day workweek and received it. After that, the rest of the United States slowly followed, but it was not until 1940, when a provision of the 1938 Fair Labor Standards Act mandating a maximum 40-hours workweek went into effect, that the two-day weekend was adopted nationwide"

Here are different workweeks around the world

As for the 9-5 timings, these 8 hours just fit nicely into a day for work, can get a 1-hour break, leaving enough time at the end of the day to do other things in your life as well.