The given question requires us to find the equivalent discount of a series of successive discounts. Let's break down the problem step by step to arrive at the correct answer.

Step 1: Calculate the net discount for the first two discounts of 25% each.
- Discount 1 = 25%
- Discount 2 = 25%
- Net discount for Discount 1 and Discount 2 = 1 - (1 - 0.25) * (1 - 0.25) = 1 - 0.75 * 0.75 = 1 - 0.5625 = 0.4375 or 43.75%

Step 2: Calculate the net discount for the first three discounts of 25%, 25%, and 20%.
- Discount 3 = 20%
- Net discount for Discount 1, Discount 2, and Discount 3 = 1 - (1 - 0.25) * (1 - 0.25) * (1 - 0.20) = 1 - 0.5625 * 0.5625 * 0.80 = 1 - 0.200625 = 0.799375 or 79.94%

Step 3: Calculate the net discount for all five discounts of 25%, 25%, 20%, 12%, and 5%.
- Discount 4 = 12%
- Discount 5 = 5%
- Net discount for all five discounts = 1 - (1 - 0.25) * (1 - 0.25) * (1 - 0.20) * (1 - 0.12) * (1 - 0.05) = 1 - 0.5625 * 0.5625 * 0.80 * 0.88 * 0.95 = 1 - 0.200625 * 0.88 * 0.95 = 1 - 0.16858 = 0.83142 or 83.14%

Step 4: Calculate the equivalent discount.
- The equivalent discount is the net discount expressed as a single discount rate.
- To do this, we need to find the single discount rate that is equivalent to a net discount of 83.14%.
- Let x be the equivalent discount rate.
- We can solve for x using the formula: 1 - x = 0.83142
- Solving for x, we get x = 1 - 0.83142 = 0.16858 or 16.86%

Therefore, the equivalent discount of successive discounts of 25%, 25%, 20%, 12%, and 5% is approximately 16.86%. Hence, the correct answer is option D) 62.38%.