As you identified and Wiktor mentioned, COUNTIF only supports wildcards.
There are many ways to do what you want, though. To name two:
=ArrayFormula(SUM(--REGEXMATCH(E9:E13, "50-03[123][012]*")))
=COUNTA(FILTER(E9:E13, REGEXMATCH(E9:E13, "50-03[123][012]*")))