Q: Transferring contacts from android samsung to iphone 5s

You don't say what you tried that didn't work so this may or may not help. One option would be via sim and your cellular reseller should be able to help you with that. Here is some information on importing them from the sim once you have them on one that fits the iPhone: http://support.apple.com/kb/HT4994

If you do an internet search for how to transfer from android to iphone there are a number of articles including the following as one example: http://www.imore.com/how-transfer-data-android-new-iphone-5s-or-iphone-5c

If you had a Google account, then you could sync your contacts with your gmail account on the phone.

I Migrated from Samsung S2 to iPhone 5S, After spending hours on how to get my Contacts Back without any third party software I found this Guide and got all my contacts into my iPhone..
I hope this guide will help you guys aswell..!
http://bit.do/Transferring-contacts-from-Android-to-iPhone