Will an AGON 49 inch monitor run off new Macbook pro M3 max chip 14 inch at 5k 120hz run on thiunderbolt

Since your M3 Max can handle 4k 240hz and even 8k 60Hz, then 5k 120Hz should not be an issue (as long as you use the right cables, HDMI or Thunderbolt4, certified to high bandwidth video), according to the Apple website they mention 4k and 8k when referring to the video modes:

Link below to the highlighted text:

M3 Max

• Simultaneously supports full native resolution on the built-in display at 1 billion colours and:
• Up to four external displays: up to three external displays with 6K resolution at 60Hz over Thunderbolt and one external display with up to 4K resolution at 144Hz over HDMI
• Up to three external displays: up to two external displays with 6K resolution at 60Hz over Thunderbolt and one external display with up to 8K resolution at 60Hz or one external display with 4K resolution at 240Hz over HDMI

Thunderbolt 4 digital video output

Support for native DisplayPort output over USB‑C (M3 Pro and M3 Max)

HDMI digital video output

• Support for one display with up to 4K resolution at 120Hz (M3)
• Support for one display with up to 8K resolution at 60Hz or 4K resolution at 240Hz (M3 Pro and M3 Max)

MacBook Pro - Tech Specs - Apple (UK)