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Annoyingly, & bafflingly, stuck on the last three, all interconnected.

52A - Fantastic grout repairs walls (5)
O???E
53D - A slovenly type raised in US city (5)
??L??
&
58A - Raise team, two short: worried? (7)
E?E???E

I incline to the notion that the answer to the last is ELEVATE, but can't parse it fully, nor does it help with 53D

gr[out re]pairs

58 elevate (elev[en] ate)

52 outre

Tulsa

Thanks to Trevor & Zozozo for their help.

Honestly, I should have worked these out for myself, but the brain seemed reluctant to co-operate.......

Thanks, again.