Afraid I misread the above poster-- I thought the question was about how two otherwise comparable HDDs with different RPMs fare.
In that case, it is self evidently true.
Increasing RPMs means your heads experience a force of 20% greater strength, as long as force and work are proportional (if all mechanical parts are identical, they must be).
It is safe to naively assume that this increases wear by 20% as well, simply because a hard drive head doesn't touch the platter during normal operation-- therefore ordinary wear is a function of drag in air, along material properties. I'm not a materials engineer or physicist, so I suppose hard drive head materials could experience discontinuous wear at standard RPMs due to properties of the material, but I think, if this were true (much less wear or much more, or little delta despite proportionally large RPM increase) you likely would not see two or more standard hard drive speeds at similar prices.
This physically self evident: the moving parts experience greater force, therefore they must experience more wear, even at the level of a single sequential write or read of the same data-- all else being equal.
Then there is heat. Heat is generally considered the primary cause of hard drive failures, and is certainly the most important factor in HDD failure that is controlled by the user.
7200 RPM drives generate more heat than 5400 RPM drives. They have to-- it's thermodynamics. More heat on identical components means decreased time to failure (of some sort of other).
Lastly, for many common workloads, 7200 RPM drives will experience greater wear as well, and it's partially unrelated to the above facts.
The most damaging mechanical operations for a hard drive are spin up, spin down, and head parking.
7200RPM RPM drives will experience disproportional exposure to, and experience of, these elements, in workloads like frequent small random reads/writes on fragmented drives (e.g. working with your amateur photography collection in a normal OS environment).
This is because, generally speaking, hard drives do not adapt their speed in sync with practical time saving (that is, your 7200 will not realize that the speed difference to random read of x data in sector y between it and a 5400 is negligible, and slow itself down), and the effective force/wear created during spin up/spin down to a higher RPM is actually not proportional. (That is, it's more than 20% in our case.)
Second, sometimes (but not always), higher RPM drives have more aggressive power saving measure implemented in firmware by the manufacturer to offset increased power draw (and often for no other reason than to have a lower power number than a competitor). This effectively means more head parking (remember the infamous WD Greens around the start of the advanced format era? I still have an opened one on my desk, the head is flayed to shreds after arm positioning errors), and more spinup/spindown (if it regulates speed based on cache flushing/cache fault or other parameters). This is doubly true where decisions are pushed to native controllers on the hard disk that aren't filesystem aware, which is becoming common (i.e. your kernel doesn't explicitly specify which blocks to write, what to cache, etc).
Often 7200 may even be worse because it does wear faster and you don't need it. Digital CCTV recording (security cameras) are a great example: low res continuous video means long and completely sequential writes. 5400 drives do this just fine.
Now, the difference overall in wear based on speed between these two standard choices is generally pretty small except workloads that happen to maximize the effect, and even there it's smaller than you would expect.
But it is true, and simply must be so based on physics alone.
**TLDR; **
THAT it is true that otherwise identical 7200RPM drives die faster than otherwise comparable 5400RPM drives is obvious.
The fact that my reading comprehension apparently sucks, and therefore I said something that sounded stupid, is less obvious-- as one can see by my downvotes.
**I know nothing about the drive models being compared, and therefore cannot comment on how they match up. I apologize for the misunderstanding and will accept the karma penance by leaving the comment up.