Club Access Awards cannot be used either for the 5-Brand Award night or the the Chase Annual Award night. Not only can it not be used for those 2 nights, it also cannot be used for other nights on the same stay as when using those non-eligible awards. You could try booking the 2 nights on all points, apply the Club Access award to those 2 nights, and then book the other 2 non-eligible award nights and hope that the hotel will grant access for all 4 nights, but I think the chances are a bit low.

See the T&C quoted below.

Explorist Club Lounge Access Awards are valid on nights for which the Member has paid an Eligible Rate or has redeemed points for a standard-room Free Night Award, Suite Free Night Award, or a Points + Cash Award, up to a maximum of seven (7) consecutive nights. Not valid in connection with any Free Night Award other than those identified above, including, without limitation, Hyatt Credit Card premium and anniversary Free Night Awards, 5-brand Free Night Awards, Category 1-4 Free Night Awards (defined below) or any other promotional Free Night Award.