Explanation

Each factor of P=5^5·15^15·25^25·35^35 is odd, so P itself is odd (it ends in 5), while Q=10^10·20^20·30^30·40^40 is even with a huge block of trailing zeros. An odd number plus an even number is odd, and no odd integer ends in zero. Hence P+Q has zero trailing zeros, option D. Counting the trailing zeros of Q alone is the distractor — the sum does not inherit them.