I know you're only wanting to hear from Verizon, but they will not provide a timeline...only provide a link that will announce the update is now available, but I came across the link below, and also read somewhere the Verizon Samsung Core Prime (I think that's what its called) is receiving the 5.1.1 update now. I know the link below is not a guarantee, but maybe a sign we will receive it sooner than later?
Here is the information on the Samsung Galaxy Core Prime phone you were referring to. http://www.androidpolice.com/2015/10/04/samsung-updates-verizons-galaxy-core-prime-from-android-4-4-...
I'm most definitely NOT a VZW employee. If a post answered your question, please mark it as the answer.
T-Mobile version doesn't have it... however they did say it is going straight to 6.0. Will probably be it's last update it'll ever see