Phone call recording did not save

5GB of space is way too little on an iPhone. You should strive to maintain 10 - 12 GB of space at all times in order for your phone to operate normally. So yes, a 6 minute recording would likely have failed to save because you have too little available space.

iCloud Storage and Notes Behavior

Free iCloud Storage (5GB)  

Every Apple ID comes with 5GB of free iCloud storage. This space is shared across all iCloud services—photos, backups, documents, and apps like Notes. In practice, most users find that this free allocation fills up quickly. Long before you reach your actual storage needs, Apple will prompt you to consider upgrading to iCloud+, which offers paid plans with larger storage capacities.

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If Notes is not enabled in iCloud

• Local storage only  

Your Notes (including attachments such as call recordings, images, or documents) are stored directly on your iPhone. They do not leave the device unless you manually back them up elsewhere.

• Storage limit  

The space available for Notes depends entirely on your iPhone’s internal storage capacity (e.g., 128GB, 256GB, etc.). This capacity is shared with apps, photos, videos, system files, and other data. If your device storage is nearly full, Notes will also be constrained.

• No sync or backup  

Notes saved locally remain on that single iPhone. They will not appear on your other Apple devices (like iPad or Mac), and they are not automatically backed up to iCloud. If your iPhone is lost, stolen, or reset, those Notes are permanently gone—unless you’ve backed up your device to a computer using Finder (macOS) or iTunes (Windows).

Storage Requirement for Call Recordings in iOS

• Format: Apple saves call recordings in the Notes app as audio files (M4A/AAC compression).
• Compression efficiency: AAC is highly compressed compared to raw WAV/AIFF.
• Typical size per minute: ~0.5– 2 MB/minute.
• For 6 minutes:
  • Low estimate (0.5 MB/min): ~ 3 MB
  • High estimate (2 MB/min): ~ 12 MB

So, a 6‑minute call recording will usually take between 3 MB and 12 MB of storage space.

I just checked that 4 minutes of VoiceMemo used up 6.8 MB of space.

Since you said you already have 5GB of space free then there should not be an issue with saving the Call recording.