Q: My iPhone 5 is not connecting to a wifi network, where as the iPhone 4 connects immediately from the same location.

Possibly but there's some troubleshooting to try.

Is the iPhone 4 running iOS 6.1.3?

What is the wifi network name?  If it's a common name, this can cause problems:  http://support.apple.com/kb/HT4450

Does it work on other wifi networks or is it just this one?

General wifi troubleshooting: http://support.apple.com/kb/TS1398