keep searching iPhone 5 signal even tho the sim card tray is out

Did you try to set it back to factory settings?

Use iTunes to restore your iOS device to factory settings - Apple Support

If this does not work, your phone needs to be checked by an Authorized Apple Service Provider or an Apple Store. Apple Support can also take care of that if you contact them.

iPhone - Contact Support - Apple Support

Turn on airplane mode. Then you can turn just wifi back on if you wish, but the cell phone radio will remain powered off. You will sometimes get the message that no SIM card is found though and as far as I know there is no way to stop that from occasionally popping up.

If you are trying to activate the phone, is the SIM card supported? Has the phone been activated with that SIM card before?

If it has been locked to a provider and you are using a different SIM, has it been officially unlocked?

Check this article for more troubleshooting:

Get help activating your iPhone

Guessing from your "yea", the phone has been activated and working with the same SIM in the past.

This could only mean that the SIM card has been damaged, can you try another unlocked device or put in a different SIM?

Has the firmware of the phone been modified in the past?

You say the SIM card "tray" is out. Perhaps you should put the empty tray in the phone and then try. Maybe it needs the tray, whether or not there's a SIM card in it.

After you tried almost everything a user can, it's about time to get the phone checked by visiting an Authorized Apple Service Provider or Apple Store next to your place, this problem might be hardware related after all.

hi andrew, is your problem got resolved. i am also experiencing same issue. it shows searching even the sim tray is out. it is not allowing to activate.let me know how you fixed it