12/27/20:
500 million miles may seem like an awful lot, but it only takes light about 45 minutes to cross that distance! So, given that short-range sensors would be utilizing mostly visible light, this would put them out of range for 45 minutes, while letting them see what was happening in the target area 45 minutes ago.
    I originally had put "500 thousand miles," but then realized that that distance would be covered in about 2.5 seconds, which would be rather less useful for stealth purposes.

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Comments from the tagboard:
12/29/20 06:24 PM
Swiftbow: Light hours/days/years are a good measure of space, but they're within less than a light hour at this distance, so it makes sense to use a smaller unit of measure.
12/29/20 06:23 PM
Swiftbow: Different units are used for different distances. An AU is quite huge, and was only ever used in Star Trek during the Motion Picture. AUs are extremely arbitrary units of measure. In this case, Dale would have had to say 5.38 AUs (or thereabouts), which would be fairly meaningless to the reader without looking it up.
12/29/20 12:45 PM
BrickVoid: As an example, the time it takes for radio waves to reach the Voyager space probes was expressed as taking "19 light-hours", not as a mileage.
12/29/20 12:42 PM
BrickVoid: Shouldn't distances be expressed in terms of astronomical units, or AU? With space there is no sure way to measure units that depend on a road or surface to reference them. I'm curious as to why you chose "miles" instead of proper astronomical measuring conventions?

Transcript
Panel 1:
Andre Peters: If we get into a fight, we'll probably need my railguns. And none of the crew has training with those.
    Most of them don't even know how to fire phasers and torpedoes!
Commodore Jeffrey Bannister: Are you saying we're not ready?

Panel 2:
Commander Dale Zurkett: Zack, I mean Mr. LeRoux, was able to program a Holodeck simulation for our weapon systems. We've run a few drills.
    But Andre's right. It's not the same.
Jeff: Are you asking to stop and do target practice?
Dale: No, we don't have time. I'm not sure what to do.
Jeff: Hrm.
SFX: *WEE-YOO*

Panel 3:
Dale: Ms. Starrat?
    Commander Zurkett here with Mr. Peters and the Commodore.

Panel 4
Lieutenant Commander Natashia Starrat: Sirs, we've started receiving long range sensor data. I think you'd better come up to the bridge.
Dale: On our way.

Panel 5
Natashia: We've detected a debris field at the distress signal's point of origin.
    The field contains metallurgical components consistent with a starship.
Dale: Life signs?

Panel 6
Natashia: Impossible to tell from this distance. There's too much interference.
Dale: Interference? Like on the message?

Panel 7
Andre: Could be. We're hitting gravity waves. They're messing with the warp field, but, so far, I can compensate.

Panel 8
Jeff: What's our distance to target?
Dale: Ten minutes. Recommend we drop out of warp at 500 million mile distance.
    If there are hostiles, it should keep us clear of their short-range sensors.
Lieutenant Zack LeRoux (aside): So much for our training time.
Jeff: Agreed.
    Sound yellow alert and man battle stations.