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What's approx. monthly cost of running something like this on lambda e.g. every 5 minutes?

If you want to access it over HTTP you will have to pay for "AWS API Gateway" which is not free.

API Gateway isn't much at that rate.

(1 month) / (5 minutes) = 8760

"$3.50 per million API calls received, plus the cost of data transfer out, in gigabytes." [0]

8760 * ($3.50 / 1000000) = $0.03.

Zero