In a large bowl, toss together the carrots, radish, cucumber, vinegar, sugar, and salt. Allow the mixture to sit for at least 30 minutes. If you're preparing this ahead of time, cover and refrigerate. Note: It will smell horrendous the following day, but will still be good to eat. You've been warned.
Preheat the grill to 450 degrees. For the burgers, gently mix the salt into the ground beef using your fingers. Shape into 5 patties and place a small thumbprint divot in the center of each one. Grill the burgers for about a minute on high heat, then reduce the heat to 350 degrees and continue to grill until liquid starts to form on the top of the burger and it easily lifts off the grate. Flip and grill until the internal temperature reaches 145 for medium rare or 160 for medium well.
To serve, place the burgers in buns and top with cilantro, jalapenos, and pickled vegetables. Mix together the mayonnaise and sriracha and spread on top.