In a party with guests who took Mirinda and Fanta, let k be the number of guests who took only Mirinda. If 5 guests took both Mirinda and Fanta, and the total number of guests who took Mirinda is 2k-1

From the Venn diagram, the number of guests who took Mirinda, $N(M)$, is the sum of those who took only Mirinda and those who took both Mirinda and Fanta.

$$N(M) = k + 5$$

We are also given the expression for $N(M)$ as $2k - 10$.
Therefore, we can equate the two expressions for $N(M)$:

$$k + 5 = 2k - 10$$

Subtract $k$ from both sides of the equation:

$$5 = 2k - k - 10$$ $$5 = k - 10$$

Add 10 to both sides of the equation:

$$5 + 10 = k$$ $$15 = k$$

The value of $k$ is 15.

We can also check the values for the regions:
Only Mirinda: $k = 15$
Only Fanta: $K-6 = 15-6 = 9$
Both: 5
Neither: 7

Total $N(M) = k+5 = 15+5 = 20$.
Using the given formula $N(M) = 2k-10 = 2(15)-10 = 30-10 = 20$. This matches.

The value of $k$ is $\boxed{15}$.