I know that the stack can automatically upgrade code on a new switch, from personal experience over many years of 5520 installs I would HIGHLY recommend setting up the new switch on a test bench and getting its image and diag code to match that of both existing switches. If the code version on your new switch is newer than the old switch/stack (and going to your screenshots it is VERY old code; your new switch will probably come with a 6.x version) I would recommend using this time to upgrade your old stack to the newest code versions, then getting the new switch up to that code version.
Following are my personal 55xx code observations:
If you don't want to try out EDM and stay with the 6.1.x code stream, I've had no issues with v6.1.4 code, although I am upgrading to 6.1.7 with no issues (stay away from 6.1.6). Note that since you have a 5.x code you WILL have to install 6.0 code first, then do the upgrade to your final 6.x code version, otherwise there can be corruption; which further underlines you DO NOT want to install 6.1.6 code as it may (from my personal experience, WILL) crash due to the switch originally having code earlier than 6.0 on it.
If you have 6.2.x running or want to get EDM, whcih is where Avaya appears to be heading for management, 6.2.3 appears to also be a stable version.