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To solve the problem of finding the number of ways to color a sequence of 5 objects using 6 colors (with no two adjacent objects having the same color), we can break down the reasoning as follows:

Step 1: Choose the color for the first object

There are 6 colors available, so we have 6 choices.

Step 2: Choose colors for the remaining objects

For each subsequent object (2nd to 5th), we cannot use the color of the immediately previous object. Thus, for each of these positions, there are 5 choices (since we exclude the color of the adjacent left object).

The number of choices for positions 2-5 is (5 \times 5 \times 5 \times 5 = 5^4).

Step 3: Calculate the total number of ways

Multiply the choices for all positions:
[6 \times 5^4 = 6 \times 625 = 18750]

Answer: (\boxed{18750})

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