Yeah it's possible, especially with an injury.
I think Manoah is probably the favorite to be the #5 unless he gets traded. The team will probably give him a mulligan but I don't know if there is going to be some sort of fight over his service time or not. He's either going to have 3 or 4 years of control left and if he can be a backend starter during that time (I think it's reasonable to expect that he can be) that's still pretty valuable. If the relationship is damaged and the team could get a 2 WAR OF with some control for him then maybe he gets dealt.
If he does get dealt then we probably need to sign a #5 to a one year deal.
As for the depth, Francis seems better than White but Francis has an option and White seems to be experiencing some sort of resurgence. And then we have Tiedemann waiting in the wings.
So all told we don't have a ton of depth but I think the SP is in great shape heading in to next year. 4 guys that never get hurt, 3 decent big league ready #5/depth options, and then one of the top pitching prospects in AAA.