Middle East - AMM layover

I am flying with RJ via Amman this Friday and having a 5 h 20 layover (19:45 to 01:05). And on my way back, I will have another layover of 5 h 30 (05:15 to 10:45).

Is it possible and worthwhile to go out of the airport and take a glance at the city?

I found information on RJ offering tours, but it seems those are full-day tours.

It's been a while since I was last there, but I seem to recall it is a long and expensive ride into the city. I might have a layover there too next month so would be interested in any up to date info.

If you do get to the city, then sure there is lots to do and see.

Madaba is closer to AMM and might be a better option for a layover if you're interested in mosaics and archaeology.

Thank you for your replies!

I chose not to go out because the weather was rather cool both times. Perhaps next time I'll undertake a real trip to Jordan and Syria.