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Depending on jurisdiction, yes this certainly is possible. There are even multiple ways to do it, in order to avoid tax election issues. You could build in a call right vesting at the 5 year anniversary of the initial issuance, or a fixed redemption construct.
If the members will be investing in multiply discrete projects with individual maturity dates and the 5-year exit is a hard deadline, a better construct would be a series LLC with each series having a fixed 5 year duration. Proceeds of each series would be distributed in the dissolution of the series itself but the LLC could maintain perpetual existence.
You'll want to be sure the LLC has not elected to be taxed as an S-corp, since this sounds like a second class of equity prohibited by the S-corp election rules. Also, are the members investing in discrete projects pursued by the LLC where they only get profits from a particular project, or do they get profits generated by the LLC as a whole? Just some initial, random thoughts.
This sounds like a private equity fund
Talk to tax.