The sidewall height of the 65 profile tyre would be 15.3cm (65% of 23.5cm). Thus the diameter of the whole wheel would be 43.2cm (17") plus 2 x 15.3 = 73.8cm.
The 55 profile tyre works out at 69cm. This reduces the diameter by 4.8cm (3.5%) so the car would ride about an inch lower, and the speedo would read 3.5% fast, assuming my maths is correct and 65 is the OE profile.
I presume you are talking about the centre diff of a 4WD as I can't imagine anyone putting odd sized tyres on the same axle. Anyway, I hardly think a diff would find it difficult to cope with one axle turning 104 revolutions for every 100 revolutions of the other axle. After all, the sole purpose of a differential gear is to allow one driven wheel to turn at a different speed to the other - the clue is in the name!
Incidentally, I saved myself several hundred pounds by fitting slightly higher profile tyres than those 'recommended' to my Audi - the reverse of what you are proposing (all 4 tyres, obviously!).
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