A question concerning the CD Rom DVD combo drive on an Alienware M5700 Model P71EN1 computer?

Please help out this computer technical illiterate disabled person with extremely limited monetary funds and ebay would have to be my go to place for a replacement part.

I was given a Alienware M5700 laptop computer and I found that the top part of the CD Rom DVD Comb drive is missing and all there is the bottom part to the drive unit; why this is, I have not a clue why it was done. And the Windows O/S it came with is not loaded due to they wiped the hard drive clean before giving it to me.

My question is, on ebay, they have several similar style disk drives, but are for the model M5500. Would the disk drive from the M5500 work in the M5700 I have?

The M5500 and the M5700 Disk Drive looks identical in every aspect including the shape, size, plug receptacle, and lock down rear bracket.

Thanks for any response.

OBTW: I have asked this question before and receive only one answer, though a positive response, I never the less would like further input prior to spending the money on the part found on ebay.

And a second answer from a second posting instructing me to go into device manager to find the type of CR Rom I needed, but no O/S loaded so cannot do that either