Hi there Bob.
To guide, you're going to need a guide scope of some kind (and a mount that will accept guide pulses, as you say... I don't know much about that EQ5, but I believe it has an ST4 port which means it should be capable of guiding already.. but again this is on the current EQ5, I don't know if you have one without the ST4 port).
Your guide scope options are either a second smaller scope with a second camera, or to use "off axis guiding" which places a guide scope between your main scope and main camera at 90 degrees. it uses a small prism to deflect light from the main scope to the second camera so it can control guiding. Either way, you're going to need a second camera (thankfully, guide cameras are fairly cheap)
The "main" guiding is usually in RA because that is the part that moves. Dec is more of a pointer and in theory should be perfectly locked onto your target, but it can drift due to a few issues, like poor polar alignment for example. So a good mount will allow guiding in both RA and Dec.
You don't need a laptop, but you'll need some sort of compute platform to control the guiding software (PHD2 is the king here). You can of course buy a laptop, but I find them a bit cumbersome, personally, having used one for a couple of years.
One option would be to get a mini-PC and mount it on or near your mount. You can remote into the PC from the comfort of your house
Or another option is the ASI Air platform, which has guiding built in (based off PHD2). If you're using a dedicated astronomy camera, you'll need ZWO cameras for this to work as it doesn't accept other brands cameras. DSLRs should work on ASI Air (though I have never tried)
As for slipping, well yes, the beefier connection, the better! When I shot with a DSLR, I used M42 connections.
and PS, your shot isn't that bad. I was expecting more trailing.
.Deep Sky Stacker.
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