The Hospital earned, but did not receive, $5000 in income from its
restricted net assets.  The income can be used for general
operations. Where should the transactions be recorded on the general
ledger?

Open a debit account
- I would call it 'Write Offs'

Medici accounting is outdated

I am not sure that Medici accounting is outdated; well, maybe it is -
but it is certainly not obsolete.

Since the monies due are unrestricted, it is a common receivable. If
the assets were investments it would probably be "interest receivable"
or "dividend receivable" but in any case is an unrestricted current
asset.

weisstho-ga