Same as what Electro said. Awesome job at getting this far man. I got some optimizations for ya too, especially including loops. Probably the most blatant (and easiest :D) example would be here.
Have you looked at the For( command? What it does is that it repeats a block of code while simultaneously counting a variable up. So if you type…
… each time the block of code reaches End, it restarts starting at For(A,1,5. The first time you run it, the variable A would be set to 1. The second time, it would be set to 2, and repeats until A equals 5 and ends. So, replace that block of code above with this.
Heck of a lot easier. It would be very possible to do this for much of your code to truncate your calculations and make them much faster and less memory consuming, if you placed your variables (B,C,D,E and J,K,L,M) on a list, and then recalled each individual element. You've got halfway there with the first calculation.
You could also probably mix all of these together into one block of code. I stored A into Ans just for the slight speed.
… or perhaps even…
Third, just some miscellaneous stuff. You don't need the "→A" with the getkey. Getkey automatically stores to Ans, so you save on some bytes and a var by deleting that portion.
Also, you got a strange Lbl 2 up top above your ClrHome. Is that intentional, or just a portion of some code you forgot to delete? The DelVar X seems out of place as well. And it's the first time I've EVER seen randIntNoRep(. xD Works pretty well though.
One more thing, it's best to take off all end quotes and parentees to save on bytes. Some people like keeping it there for OCD purposes though, which is totally cool.
You seem like you have a pretty good grasp on TI-Basic though, which is fantastic. Hope ya keep up your good work! Just to summarize my changes for you real quick…
Output(6,2,"PRESS ANY KEY
"ACE 2 3 4 5 6 7 8 9 10 JACK QUEENKING→Str1
"SPADES DIAMONDSHEARTS CLUBS →Str2
EDIT: Bugfixes. Should work perfectly fine now. The large names though look bad, especially if you get a QUEENS. I'd recommend truncating them to A,1,2,…J,Q,K, and then scooting it over to allow for the space between the number and "OF".