Running the pump might stir up algae, but it doesn't cause it.
Read the Best Guess page linked in my signature -- odds are, your CYA level is so high, that an FC level of 5 - 6 is LOW, not high. If you've been using trichlor or dichlor to chlorinate for an extended period of time, this is almost certainly your problem.
You'll need a Taylor K2006 kit from Amazon to test, and then manage your pool. Strips are inaccurate, and are HORRENDOUSLY inaccurate at testing CYA (stabilizer).
Links for test kit info, and my Best Guess chart, are in my blue signature block.
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