Make sure there's no solder on the outside of the bullet connect. Then use a vice or something so that the plastic housing is supported, but the wires can dangle underneath. I use a hammer and a punch to tap the connector into the housing.

Also check the taper on the connector to make sure it presses in the way you think it should. Some press in from the front, some press in from the back.

Easiest solution is to switch to XT90 plugs.

Are you soldering with a set plugged together? When I solder just one end of plugs I find the heat will allow the pins to drift out of alignment a lot. Plugging in another empty plug helps prevent that. Not really ec5 specific as I use xt60's.
1) tin the wires
2) Tin the cups
3) Apply the iron to the outside of the cup and apply a small bit of solder to improve contact
4) when the cup is liquid, start pressing in the wire, it'll heat in no time.
5) remove heat

Works all the time for me. #3 is super important in my experience or I can wait forever for heat to transfer if the tip isn't squeaky clean.

I feel your frustration. this is what I did for EC 5'............I drilled a hole big enough in a table board piece of junk and fitted the ec 5 ends so they wouldn't move kind of like a vise but just enough to get it in the hole to solder. I then tin the wire. 1 at a time .not both to avoid shorting it out. tin the end of the ec 5 . NOW its important to keep the soldering tip tined or heat wont transfer. after cleaning I tin the solder tip then touch the ec5 end to get it hot sticking the tip in the hole where the solder is about to liquify . when it does stick the wire in the hole. stick the tip to the wire and melt the wire tinning to the ec5 when it melts stop and let it cool for 20 seconds and then pull it out of the hole start it in the ec5 slot where it goes and tap it in with a small screwdriver. it will click in and now on to the next one. Ec 5's are for 4 and 6 cell BUG draw amps. good luck

FYI, the new stock of Dynamite EC5 connectors have the half cup soldering posts like the XT60's. Makes it a lot easier to solder, well worth the price premium of the name brand connectors.

FYI I just soldered a pair of the Dynamite brand connectors with the half height cup on one side. Soldered very easy but the hobby shop said they are pull through connectors, this was bad advice, I tried a brass punch with the connect sitting on top of my vise and it wouldn't seat. Then I pushed into the back of the body and seated with a small flat head and gunsmith hammer, they went in easy. Might be nice if they printed basic instructions on the package.

What kind of solder tip are you using?
too small and not enough heat is transferred quick enough, too large and the heat can melt the connector.

My basis is the tip width should match the cross section of the wire and pin., The gauge of the said solder tip needs to be equal to or slightly less in diameter overall at the tinning. Thou thru my own trial snd error I am now using a rather wide screw driver type tip on my iron now and recommend a minimum of 70watts. I have used a wide range of tips and whatnot however rarely on anything that required large ones. Back in 1/10 days I didn’t have to use more than 40watts and a 2mm tip.

This is spot on info right here. I've been soldering a LOT of connectors lately with a really good iron and the pointed tip was beat and I found a flat blade, like a screwdriver tip, that was laying around and it literally changed my soldering life. I didn't think it would have that much of an impact.

Also, we use ic5 connectors almost exclusively now. Easy to solder and work with ec5. I may change out all my xt90 at some point

it's called a chisel tip. back to the OP, check out post at the top of this forum.
How to solder correctly (a not so brief lesson)

chisel tip over the pencil tip will make a giant improvement in your soldering.. pencil can not hold heat temp as long as a chisel tip..

Now stop being a Donkey please

For what is being done the correct tip is the chisel tip, not the screwdriver tip which features a much narrower tip and has more heat loss than the chisel tip. Conical, wedge and most other tips have no place in the basic soldering world that rc hobbyists practice in. Unless you're doing repairs inside your esc or other 2M applications you can put a 3-4mm chisel tip on your iron and forget about it for a decade. I solder for a living doing aviation electronics repairs and use the gamut of these daily.

and a nice clean solder joint will allow the plug to slide back in housing...