Let the number of cookies Rohani baked be $x$.

Since Nora baked 5 times as many cookies as Rohani, Nora baked $5x$ cookies.

The average number of cookies they both baked is 360, which means:

$\frac{x + 5x}{2} = 360$

Simplifying the left side:

$\frac{6x}{2} = 360$

$3x = 360$

Now, solve for $x$:

$x = \frac{360}{3} = 120$

Since Nora baked 5 times as many cookies as Rohani, the number of cookies Nora baked is:

$5x = 5 \times 120 = 600$

So, Nora baked 600 cookies.

Would you like more details or have any questions?

Here are 5 related questions you might find interesting:

1. If Nora baked twice as many cookies as Rohani, how many cookies did Rohani bake?
2. What would be the total number of cookies if both Rohani and Nora had baked the same amount?
3. If the average number of cookies they both baked was 450 instead of 360, how many cookies did Nora bake?
4. How many cookies would Nora have baked if she baked 10 times more than Rohani?
5. If Rohani baked 50 more cookies, how many would Nora have baked to maintain the same ratio?

Tip: When dealing with averages, always remember to sum the quantities and then divide by the number of quantities to find the average.