The LG Ultrafine 5K Display connects via Thunderbolt 3. To give both the display and the Breakaway Box/Puck each maximum bandwidth, connect them to independent Thunderbolt 3 controllers, if possible.
The 13" Macbook Pro with Touchbar, 15" MacBook Pro, and iMac Pro have two independent Thunderbolt controllers. Connect the Display and the Breakaway Box/Puck to ports on different sides.
The 13" MacBook Pro without Touchbar and the iMac with Retina display and the have only one Thunderbolt controller. The LG Ultrafine Display will reserve all the bandwidth it needs, and the Breakaway Box/Puck will be allocated the remaining bandwidth, which may affect performance of the Breakaway Box/Puck.
A Breakaway Box/Puck will not accelerate games on the LG Ultrafine 5K Thunderbolt 3 display. Professional applications that use an external GPU generally do not depend on which display is used.