What are some family-friendly posts to be assigned to next as an E5?

To add to this response, it isn't the base, it's the unit type. You're a fire support specialist, you'll probably always be in a Divisional BCT or Artillery formation. The required capability is requested by the Combatant Commander and the Joint Chiefs source the request for Forces and direct the appropriate or available forces to be deployed by the service tasked. It has little to do with bases but the Army Forces Generation Process and dwell time.

You can only be assigned where there is a slot on an authorization document: the Modified Table of Organization and Equipment (MTOE), Table of Distribution and Allowances (TDA for non deployable organizations), or JOint Manning Documents (JMD). You're junior, so a JMD slot is highly unlikely. Also JMDs are forward deployed based as a PCS as much as they are Not. TDA units are particularly career enhancing and tend to Ben more senior unless you are there MOS immaterial.

Anywhere in Europe is good, Carson, Campbell, Irwin (I'll explain) are probably good. Irwin doesn't deploy, but you are on rotation every month, but it is hyper predictable. Schedules locked in with contracts. Dedicated block leave. Warning. Families either love it or hate it. Many families come back with more kids than they arrived with. It's isolated, but the time you do have is with family....because of the isolation.