Why does vehicle ding five times with no warning lights showing?

Unlikely to see a 'Ding Ding' fuse, but you do have 600 other fuses and modules. :>D

Ford Expedition (U222; 2003-2006) fuses and relays

https://fuse-box.info > ford > ford-expedition-u222-20...
Passenger compartment fuse panel - Cigar lighter (power outlet) fuses in the Ford Expedition are the fuses ?37 (Cargo area power point), ?39 (Instrument ...

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what do you mean dings is there a ringing,beeping sound in the passenger compartment or is this a tapping sound from the engine

Buckle seat belt prior to starting.. and see if it still does it ? Another issue may be an ABS or Engine Fault Light or Air bag system (fault warning).. ie.: a stored code in the computer the vehicle is tiring to alert you exists...

Safety systems can be surprising...my first inspection would be to check the fluid level in your brake master cylinder...the warning light may not be working...Hope this helps.

It sounds like it thinks the key is still in it all the time. Try turning the key forward to the on position, but not running, so the dinging stops. disconnect the battery. Remove the key completely and reconnect the battery.

Here's a link to your lightning bolt dash light and what it means. Throttle Control Warning Light

are you sure you haven't inadvertently set the speed warning on the onboard computer ?

one of the door/van loading door switches has failed it thinks a door is open so the the interior light stays on and the door open warning will ding the interior light should have a switch to disable it or take out the bulb but you cant stop the dinging until you find the faulty latch switch and fix it

is your vehicle equipped with a passenger side airbag off switch you turn w/ the key?turn it on

I had the same problem with my 2006 Jeep Liberty Renegade. I shared with the Jeep service tech what I found on the internet regarding this problem. I was having the gas cap sensor to display and soon after other sensors were lighting and dinging and some times dinging without any indicator and vice versa. the service tech said he was not aware of any such complaints and recommended a diagnostic which found no trouble codes and recommended to change to the gas cap. I did so and no sooner than paying almost $100 for the service and returning home the same thing started happening again. I returned my vehicle and they called the Chrysler/Jeep service tech who obviously was aware of these complaints [Service Bulletin #14-001-06] and recommended the following: A complete system reboot. Disconnect the battery cables and short together for 15 seconds. If message returns then the problem may be with cluster. I have not had any dinging or gas-cap sensor display since this was done.