My iPhone 5 will not connect to the mobile network and just says "Searching..." in the top left hand corner of the screen, any ideas?

If that happened to me, once I convinced myself that the antennae did not have anything around them that might cause interference (like another cell phone), I would contact my cellular carrier.

Here's how to contact them:

Contact a mobile carrier

Try to manually search for your carrier. Go to settings > carrier > turn off automatic. Then you search for your carrier and find out if it is able to detect your carrier.