I have backed up my iphone 5s contacts to iCloud however not all contacts are saved. How do I ensure all contacts get backed up?

Welcome to the Apple Community.

Before continuing, contacts are synced not backed up, there's a fundamental difference, you need to back them up as well.

Please try the following…

1. First check that all your settings are correct, that contact syncing is checked on all devices (system preferences > iCloud on a mac and settings > iCloud on a iPhone, iPad or iPod).
2. Make sure the contacts you are adding are added to your 'iCloud' group and not an 'On My Mac', 'On My Phone' or other non iCloud group (you can do this by checking in groups), non iCloud contacts will not sync.
3. If you are sure that everything is set up correctly and your contacts are in the iCloud group, you might try unchecking contact syncing in the iCloud settings, restarting your device and then re-enabling contact syncing.