The maximum number of apps for free development profiles has been reached. Xcode 11.5

I had the same exact issue, even though I uninstalled all apps installed through Xcode. I found out that after updating to Xcode 11.5 and iOS 13.5, some of the other apps (not developed by me) are counted toward the limit.

Open Console app on Macbook and catch logs while trying to install an app from Xcode. Under Devices on the left > Choose your iPhone device > Then search for MIFreeProfileValidatedAppTracker and something like:

[MIFreeProfileValidatedAppTracker _onQueue_addReferenceForApplicationIdentifier:bundle:error:]: 182: This device has reached the maximum number of installed apps using a free developer profile: {(
    "<bundleid>",
    "<bundleid>",
    "<bundleid>"
)}

Instead of <bundleid> there are gonna be concrete ids that are counted toward free app limit. I found out, which app are those, deleted them and everything worked like a charm after that.

In Addition to Artur Peplinski answer, all apps effected are offloaded apps. Apple include a feature on iOS 11 that automatically offload unused app after 14 days. You can disable this feature in the iOS settings. If you load them again or delete them, it works

This is not a bug. Apple restricts free developer accounts, permitting the installation of only three apps on a device.

An easier way is to delete apps through the Xcode devices window, instead of searching through the log file. In Xcode 13.1, the devices window is accessible from the Window > Devices and Simulators menu item, or by using the shift + command + 2 keyboard shortcut.

Use the delete button to remove apps under the same account.

When targeting devices running iOS 13.3.1, tvOS 13.3.1, watchOS 6.1, or later using a free Apple Developer account, app extensions incorrectly count against the limit of three apps installed simultaneously. When this happens, Xcode reports an error: “The maximum number of apps for free development profiles has been reached.” (59264389) (FB7568073)

Workaround: Delete apps signed with your free account from your device and also remove any associated provisioning profiles from the device using Xcode’s Devices window. If your app contains more than two app extensions, remove them to remain under the three app limit.

https://developer.apple.com/documentation/xcode-release-notes/xcode-11_4-release-notes