How do i delete a sent text to another phone from a iphone 5c?

As for your situation, you can recover the lost contact on iPhone with iOS Data Recovery. Just follow the below steps to do that.

Step 1 Connect your iPhone 5c to the computer
So as to recover deleted contacts on iPhone 5c, you should free download Leawo iOS Data Recovery on your computer first, and run it on the computer, and then use a USB cable to connect your iPhone 5c to the PC.

Step 2 Start to scan your iPhone 5c
Once your device has been detected by the iPhone 5c contacts recovery program, a "Start" interface will show, just click "Start" to scan your iPhone 5c.

Step 3 Preview and choose contacts on iPhone 5c
The scanning will only last for several minutes, after scanning, you are able to see all the different types of files listed in neat categories on the left sidebar. By clicking "Only display the deleted items" option on the left corner of the interface, you'll see all the files that have been deleted from your iPhone 5c. Just click "Contacts" type to preview and then tick the single contacts you want to recover from iPhone 5c.

Step 4 Recover deleted contacts on iPhone 5c
After preview and selecting files, tap on "Recover" button on the right corner, then you'll see a pop-up window for you to choose saving location for the files. Click "Open" to browse the computer file explorer and choose a saving folder on your PC, then click "Go" to start to recover contacts from iPhone 5c.

This is just an example to show you how to recover deleted contacts from iPhone XS Max and other iPhone models directly. Actually, Leawo iOS Data Recovery could help you recover deleted contacts from iTunes, and retrieve contacts from iCloud as well.

For more methods, check: How to Recover Contacts from iPhone

Make sure sim card is seated properly

remove sim card and gently clean gold contacts with a pencil eraser or qtip dipped in alcohol..let dry be for re inserting

contact service provider and have a new sim card sent to you

i dont own an iphone sadly, but i looked at my wife's and sons and there does not seem to be a way to go to the top of the list faster then just scrolling, though he did say he remembers a text app that is suposed to help log them and let you search by date, srry i cant be any more help than that

To my knowledge, you can use the iOS Data Recovery to help you recover the deleted text message.

How to Retrieve Deleted Text Messages on iPhone 2018 update

Had you backed up the iPhone 5 when you found the messages are lost?
Go to "Preferences" > "Devices" in iTunes to check whether you had backed up the iPhone 5 with iTunes.
Tap "Settings" > "iCloud" > "Backup" to see if the iCloud backup is the most current.
If you have iTunes or iCloud backup and the backup file is latest, just restore the iPhone 5 with iTunes or iCloud.
If the backups are out of date, and you don't want to lose the data created after the backups, try to extract the messages from iTunes or iCloud backup using an iPhone backup extractor.
If no backup is found, download the best iPhone data recovery software to scan the data on your iPhone and recover the deleted messages from the iPhone.

The iPhone 4 makes it possible to be interconnected and synced up, so you do not have to fear losing data or files again if you engage in some preparation. Accidentally deleted items from your iPhone 4, or even breaking or losing the device, does not mean that your data are gone for good.

Learn how to perform iPhone data recovery using software.