When were the pictures taken? Late last summer? I see some crabgrass and it looks like some dormant fine fescue that may have been suffering from the heat. Mowing higher will definately help. U may have to do some seeding this fall because rye and fescue are clumping grasses and will not spread much on their own. Put down a crabgrass pre-emergent a few weeks before the first mowing and apply 2-3 rounds of high nitrogen sept-nov. No need to fertilize stressed cool season grasses in the heat of summer unless u are getting adequate rain.
Core aeration would definately help. Do it when it's cool and the grass can recover.
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