Can I retrieve the data from my burned out HD?

I have an external 5" HD in an external enclosure. A while back, the power adaptor to the enclosure overheated and the HD stopped working. No noise from it whatsoever, not even the usual laboured spinning you get from a broken HD. I tried it in a different enclosure with the same result so presumably the power socket on the HD got fried too.

Is there any way I can find out whether the data has survived and retrieve it to transfer to another HD? If the only way is something expensive that involves sending it to specialists then I can live without it but if there's something not too expensive and safe! - that I can do myself (without requiring too much technical knowhow) then I might be willing to give it a try.

I'm presuming the answer to this type of enquiry will be much the same regardless of make and model but if I'm wrong then I can open up the enclosure and check the HD specs.

Thanks

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