Just get my new iPhone 5, is there a way to transfer text messages from my old Android to iPhone 5? Thanks.

Tried Backuptrans Android SMS to iPhone Transfer?

You need to use a andorid data manage or phone transfer to copy sms from android to iPhone

Transfer Text Messages from Android to iPhone 6/5S/5/4S
http://restore-samsung-contacts..com/2014/06/transfer-android-samsung-sms-to-iphone.html

Transfer and Print Text Messages from Samsung to Computer
http://recover-android-sms..com/2014/08/transfer-restore-samsung-sms-messages.html

what about transferring text messages from one android phone to another?

Here comes a good news! We can backup any data on iPhone/iPad/iPod to iTunes, Computer and Back in a simple way!
With iPhone Data Transfer software, you can transfer videos, music, photos, playlists, contacts and more from your iPhone, iPad and iPod as easy as pie.
how to transfer data between android and iPhone
If you lost data of your iTunes library, replaced your computer or even re-installed OS and forgot to back up your iTunes library, you might have lost your media on iTunes. Even if you try to sync with your iTunes account from your iDevice, it will almost surely be wiped out.
how to transfer data from android to iPhone
Okey, all you need is iPhone Data Transfer program to restore everything in your iTunes library with ease.
If you want to have a try, you can follow the steps.
how to transfer contacts from android to iPhone