Airport to airport

Where does the flight into LHR originate?

What is the destination of the LTN departure?

What time of year ( weather issues either at your origin or what you may encounter in London)

Depending on how much ( or if) border crossing is involved and checked bag considerations the answer probably varies based on the details of whether 5 hrs is prudent./ adequate.

I looked at the National Express site and a direct bus takes about an hour. They run frequently, usually around every 30 minutes but check the schedule, and if your flight arrives on time, I can’t imagine why you wouldn’t make the transfer in time. Traffic could have an impact.

There are undoubtedly tube/train options as well.

Making the 17:00 flight at Luton is doable but on the other hand very risky too. You don't have 5 hours as check-in/bag drop for your onward flight will close between a 30 mins and hour mins depending on the airline. Also from wheels down on the runway @ LHR to being out side the terminal will take 40mins to a hour and getting around or through the Smoke is always time consuming. So, in all reality you have 3 hours max to get between the two airports - with a fair wind its a two hour journey. As already mentioned already there are a number of variables such time of the week, traffic and weather among other things that can blow one astray. Thats putting aside if your inbound is on time or not - all, things considered the 21:00 is the safer option. It is better being a bit early and sitting airside with a beer, than stuck on the M25 or on a train anxiously looking at ones watch.

The rail route takes 1 3/4 hours.
Elizabeth Line to Farringdon, Thameslink to Luton Airport, DART shuttle train from the train to the airport.
Carol is being very optimistic, the later flight is far preferable.
All it needs is roadworks or an RTA on the M25, or a minor incident on the train line and you are snookered for the 1700 flight.
National Express themselves say you must allow 3 hours from your coach arrival time at any airport to your flight departure time.
That is effectively impossible for the 1700 flight.

Five hours is more than enough time - Underground to King's Cross St Pancras, train to Luton Airport Parkway (from adjoining St. Pancras) then DART or shuttle bus to the airport. Well under two hours at that time of day so you even have some room for delays

Five hours is more than enough time - Underground to King's Cross St Pancras, train to Luton Airport Parkway (from adjoining St. Pancras) then DART or shuttle bus to the airport. Well under two hours at that time of day so you even have some room for delays

What nonsense,

The shuttle bus has stopped operating now that DART is fully operational at Luton, as of 31 March. The buses are in hot storage for now in case of issues with the DART but are not operating in tandem with it.
Why take underground when Elizabeth Line is faster, which takes the time stated. 45 minutes to Farringdon, say 5 minutes to change, 35 minutes to Luton Airport parkway, 5 minutes to change, 4 minutes on DART.- that is 1 hour 34 minutes in transit assuming no wait time.
There is check in and security at Luton (allow 2 hours), and immigration at Heathrow/walking to the station/ticket buying.
That is if all goes well and the TA flight is not delayed. There is a maximum of 15 to 30 minutes leeway here- that is a huge Las Vegas style gamble.

"Five hours is more than enough time"

The issue is, the OP does not have 5 hours.

Check-in/bag drop for thier onward flight could close a hour before departure and airlines timing are based when the wheels hit the runway, so the inbound aircraft has to taxi to its stand and all the formalities of immigration, luggage collection et al. Its not known what day of the week the OP is travelling Midday Friday and Sunday will be very different expierances. I as I said it is doable, but very risky with no room for manoeuvre in the event of something unexpected happening.

You don't want to start your trip stressed. Take the later flight. I would rather hang around the airport with a nice drink than have to pay extra and figure out a next-day flight or worse still stay overnight in Luton. You could get a private driver but you won't get there any faster. Just maybe a little more comfort.

The National express website states: "The absolute minimum time with no contingency between flights that you should contemplate making a transfer between Heathrow and Luton is 4.5 hours. The route of about 35 miles (56km) between Heathrow and Luton is along heavily congested motorway/freeway. Mondays to Fridays between 6.30am and 10am and 3.30pm and 7pm traffic congestion is routine, expect delays of 15 minutes or more. There can also be severe congestion late Sunday afternoon/ early evening. But at anytime the slightest incident can bring the road to gridlock. The approach road to the passenger terminal at Luton is also prone to traffic congestion delays."

By the way I can echo the bit about the approach road to the airport. It is renowned for that.
It is the only major airport I know of anywhere where hordes of people walk in, at all hours of the day and night. They are dropped off at the base of the hill and walk up what is a substantial hill. You can go there at 4am on a winter morning and there are scores of people walking up.
Part of that of course is due to high parking and drop off charges, but part is congestion.
The new DART shuttle train, with it's high charges, is unlikely to change that.

Let's make this succinct:

If the gods are on your side, and everything runs on time, you could make the 5 PM flight.

But with one hiccup, it could be very costly as you would probably have to buy new tickets at the last minute rate.

I'd probably go with the 9 PM flight. However, if I got to Luton in time for the 5 PM flight, I might ask if they could switch me to that earlier flight. The worst that could happen is they say no.

I agree that a 17:00 flight is optimistic, and while you might make it there is a very real risk you won't.

But I'm going to suggest a third option, spend a night in London and continue to you final destination the next day. And afternoon in London will be more fun than an afternoon at Luton. And a 21:00 flight from Luton will mean a very late arrival. Or, find a flight from Heathrow.