To determine if Emanuel's lawn mowing cost will be $90 more than Kyle's, let’s go through the problem step-by-step.

1. Define Variables for Lawn Areas: Let $x$ represent the area of Kyle's lawn in square meters. Since Emanuel's lawn is 5.6 square meters larger, the area of Emanuel's lawn is $x + 5.6$ square meters.

2. Define the Cost Function: The cost of mowing a lawn of area $x$ is given by the function: $f(x) = -15(-x) + 25 = 15x + 25$ So, $f(x) = 15x + 25$.

3. Calculate the Cost for Kyle’s Lawn: The cost for Kyle's lawn, with area $x$, is: $f(x) = 15x + 25$

4. Calculate the Cost for Emanuel’s Lawn: The area of Emanuel's lawn is $x + 5.6$, so the cost to mow his lawn is: $f(x + 5.6) = 15(x + 5.6) + 25$ Expanding this: $f(x + 5.6) = 15x + 84 + 25 = 15x + 109$

5. Find the Difference in Costs: The difference in cost between Emanuel's and Kyle's lawn mowing is: $f(x + 5.6) - f(x) = (15x + 109) - (15x + 25) = 109 - 25 = 84$

So, the difference in cost between Emanuel's and Kyle's lawn mowing is $84, not $90. Therefore, the cost of mowing Emanuel's lawn will not be $90 more than the cost of mowing Kyle's lawn.