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In this scenario, we begin by understanding how deductibles work. A deductible is the amount a policyholder must pay for covered medical expenses before their insurance kicks in. In this case, the family has a deductible of $6,000 and has already paid $5,000 towards this deductible.

For a medical procedure that costs $1,500, the family has already paid $5,000, so they are responsible for the remaining $1,000 in order to reach the deductible limit of $6,000. The logic here is straightforward: the total deductible of $6,000 minus the amount already met ($5,000) equals $1,000.

Therefore, for the procedure costing $1,500, the family will need to pay this $1,000 out of that cost, which is still less than the total cost of the procedure. After paying the $1,000, the family's deductible will be met, and they can then submit any further costs for coverage within the insurance plan, depending on their coverage details beyond the deductible.

This answer clearly illustrates how deductibles influence out-of-pocket costs for medical procedures.