This is most likely a shutter delay setting, not the flash itself. The flash fires when the shutter opens, so if there’s a pause before the shot, the camera is delaying the shutter release.

On the Nikon D5200, common causes include:

• exposure delay mode enabled (Custom Setting d5)
• self-timer mode selected
• red-eye reduction flash mode, which adds a short delay before the exposure
• remote control delay mode for the ML-L3 remote

Auto mode may override or avoid some of these settings, which is why it can seem normal there.

Check your release mode and flash mode first, especially red-eye reduction or self-timer. If those are off, look in the custom settings for Exposure Delay Mode. The D5200 reference manual is also helpful because it explains these timing-related settings in more detail.