Both.
Step 1: Establish a realistic threshold pace. Do a 20 minute run where you run in one direction for 10 minutes, turn around and come back in 10 min or slightly faster, without suffering. If you come back too fast, say 9:15 and it still feels pretty easy, you went too slow on the way out. If you make it back to the start in 10 min, but are barely hanging on, you went out too hard. If you can’t make it back to the start in the time you went out, you started WAY too fast. Do this session a few times, until you get it right. For you, let’s pretend you end up doing this at 6:05 pace
Step 2: Do 6-8 x 1 min on one min off. As the main body of your workout. If 6:05 was the pace you were comfortably hitting for your 20 min threshold effort, pick it up to maybe 5:50 pace for the ON minutes and, here’s the key, only slow down to what your normal easy pace is. So, maybe you have a workout where you alternate between 5:50 and 7:30 pace for 16 minutes.
Step 3: start doing both of these workouts on a weekly basis and follow each session with some easy reps at 800-1600 RP with full recovery.
Step 4: as your fitness improves, you can either: keep the same paces and add volume, or keep the same volume and add speed. Since you’re trying to make the jump from racing 3 miles to racing 5 miles, I’d opt to increase the volume. So, at the beginning, you might do workouts like 20 min at 6:05 pace followed by 4x200@32 or 8x 1 min at 5:50 / 1 min at 7:30 followed by 3x400@72. After a few months, those 20 min sessions might have turned into 30 minute sessions and the 8x1/1 might have turned into 12x1/1
As a side note, you seemed a little confused by the TEMPO / THRESHOLD. Terms. Generally, people talk about threshold as the pace that is right at their Lactate Threshold and sessions are around 20 minutes for a continuous run, while tempo is somewhat slower and can be done for longer periods. So, you might see Mike Smith’s NAU guys do 40 minutes “sub threshold”, which is the same as other coaches saying 40 minutes Tempo. For you, as stated earlier, you will probably get more bang for your buck by lengthening your threshold into tempo efforts as you gain fitness. If you progress properly, you’re hypothetical 6:05 threshold pace will eventually become your tempo pace and your hypothetical 5:50 fartlek pace will become your threshold pace.
Step: 5. Once you’ve had a few months of consolidating at the paces you started at, you can gradually start increasing the speed.