In a medium bowl, combine soy sauce, vinegar, lime juice, oil, and ginger. Add pork to marinade, turning to coat. Marinate at room temperature for 30 minutes (or refrigerate, up to overnight).
Heat grill to medium-low; lightly oil grates. Lift tenderloin from marinade; discard marinade. Grill, turning occasionally, until an instant-read thermometer inserted in thickest part of pork registers 145, 18 to 20 minutes. Remove from grill. Tent loosely with aluminum foil; let rest 5 minutes before slicing.
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