Do you just want to run 1 mile at 5:30?
I did two types of workouts last year while dealing with an injury that kept me from running more than about 6-7 miles a week. Funny though, speed work didn’t aggravate it.
I’ll preface this with these worked for me, may not necessarily work for anyone else.
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Run a mile. All out. Each week. You don’t know how fast you can run a mile unless you do it.
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200m with 30s rest at 40s or less (<= 5:20 mile pace). Start with 16 and build up to doing 24+. Start at 40s, basically working on trying to hit each one at the same time. You’ll notice after few weeks you’ll be running faster than 40s without trying.