Ever-Rest sells its mattresses for $1,085 less 25%. This means the amount of discount is 25% of $1,085, or 0.25*$1,085 = $271.25. The price after the discount is 

$1,085 - $271.25 = $813.75.

Now let's calculate the net price at which Posture-Perfect sells its mattresses.

The price after the first discount is $892 - 20% of $892, which is

$892 - 0.2*$892 = $713.6

The price after the second discount is $713.6 - 5% of $713.6, which is

$713.6 - 0.05*713.6 = $677.92. This is the net price of Posture-Perfect's mattresses.

To match this price, Ever-Rest would have to discount their already discounted price by the amount of

$813.75 - $677.92 = $135.83.

The percentage this amount makes of $813.75 is

`($135.83)/($813.75) * 100% = 16.69%` (rounded to two decimal places)

The Ever-Rest would need the second discount of 16.69% to match the Posture-Perfect's net price.