Building on what Emma said, if you’re comfortable going a bit deeper, you might want to consider a third-party app store—though this requires jailbreaking your iPhone 5c. Jailbreaking opens up options like AppCake, TutuApp, or Cydia, where you can sideload IPA files—the iOS equivalent of Android APKs. These stores often keep archives of older app versions compatible with iOS 10.3.3.
This method gives you more direct control to install exactly the version of Spotify you need, but it’s riskier: jailbreaking can expose your phone to malware, certificate revokes, or even bricking. If you’re involved in app QA or development across legacy devices, you can also use LambdaTest’s real device cloud to test apps on iOS 10.3.3 without risking your own device, before you decide whether to jailbreak or try unsupported sideloading.