If you have valid license you may install 10.5 & 2018.3 at the same time on your machine. You also can run both applications. The license covers all application versions before expiration and maintenance date.
And yes, you will. Also if you are not using features that were released since 10.5 in your 2018.3 workbook - you will be able to downgrade your workbook (down to 10.2) so the user with 10.5 version of the software will be able to open it.
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Thank you for the prompt reply and complete answer!