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@BobJacobsen's comment about the MX Missile (and protests) in the 1980's got me clicking in Wikipedia, which led me to the Minotaur IV launches, the most recent of which seems to be ORS-5 or "SensorSat", a roughly 140 kg spacecraft built by MIT to "keep an eye on GEO".

Ran in a 5-stage configuration, using an extra Orion 38 motor to put ORS-5 in to an equatorial orbit.

This configuration would have normally been four stages, the additional stage was needed for the delta-v to make a plane change equatorial LEO.

It turns out I've asked a previous question about this launch: What inclination change could the 5th stage Orion 38 motor provide ORS-5 (SensorSat)?:

The screen shot and block quote below are from Orbital ATK's Mission Update: Minotaur IV ORS-5 Launch. ORS-5 or "SensorSat" is a technology demonstration for a class of satellites that will sit in LEO and keep an eye on the GEO belt for any "debris" which I suspect means pranksats or worse. ORS-5 will sit in a 600 x 600 km equatorial LEO.

See that question and the answer there for several more links.

Question: In the 21st century or thereabouts, how often are five stages used to put a relatively light spacecraft into low Earth orbit? Even for a heavy payload, is it quite rare to use five distinct stages to LEO?

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5 stages is extremely rare -- in both the 20th and 21st centuries. Most modern launchers are two-stage-to-orbit, sometimes with a third stage for transfer to geosynchronous orbit, or added boosters firing concurrently with the first stage for increased payload capability.

Any 4- or 5-stage LEO launcher is almost certainly going to be based on solid rockets as opposed to liquids. The delta-v for a given launcher stage is directly proportional to the specific impulse of the engines, and secondarily affected by the stage mass ratio (i.e. the fraction of the stage mass that is propellant rather than tankage & structure); solids have about half the specific impulse of hydrogen-oxygen engines, and worse mass ratios than kerosene engines. Thus, a liquid stage can easily achieve almost twice the delta-v performance as a solid rocket stage; since delta-v from launch to orbit is nearly independent of anything else, you simply need to stack more stages to reach orbit on solids.

ASLV and Minotaur V had five stages.

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  • $\begingroup$ I wonder if this in fact the only example in the 21st century. Thanks for your perspective! $\endgroup$
    – uhoh
    Commented Jul 18, 2018 at 7:12
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    $\begingroup$ With the caveat that the definition of “stage” is somewhat fuzzy, it’s the only modern orbital 5-stager I know of. You can view Saturn V/Apollo as 6 stages... $\endgroup$
    – Russell Borogove
    Commented Jul 18, 2018 at 13:58
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    $\begingroup$ India's ASLV launcher put 150kg into orbit on 5 solid stages, but last flew in 1994. $\endgroup$
    – Russell Borogove
    Commented Dec 9, 2018 at 0:37
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    $\begingroup$ That seems like it belongs within your answer. $\endgroup$
    – uhoh
    Commented Dec 9, 2018 at 0:55
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    $\begingroup$ @JoeJobs More stages = more points at which you discard dead weight (empty fuel tanks/solid rocket casings). This means better payload mass ratio, but there are diminishing returns due to the weight of interstages and additional engines. For liquid-fueled rockets, the tanks are lightweight, and specific impulse high, so the tankage weight penalty is minimal, so 2STO is the usual modern baseline solution. Solids have thicker casings (thus greater dry mass),and lower specific impulse, so it's harder to get a lot of ∆v out of each stage, hence they use more stages. $\endgroup$
    – Russell Borogove
    Commented Oct 5, 2020 at 19:06

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