Well, the first 5 primes are 2, 3, 5, 7, and 11. And 11 is a non-trivial palindrome.

So, 11 is the product of the first 5 primes divided by 210

Also,

22 is the product of the first 5 primes divided by 105

33 is the product of the first 5 primes divided by 70

55 is the product of the first 5 primes divided by 42

66 is the product of the first 5 primes divided by 35

77 is the product of the first 5 primes divided by 30

So, these are 6 obvious solutions. It looks to me like X = 5, Y = 30 might be the smallest Y value for the smallest X value