DTFT fourier transform (modified property)
Hint:

Note that you can express your signal as

$$x[n]=(n+1+4)\left(\frac{7}{45}\right)^{n}u[n] = (n+1)\left(\frac{7}{45}\right)^{n}u[n] + 4\left(\frac{7}{45}\right)^{n}u[n] $$

So now you have the sum of two signals:

$$x_1[n]=(n+1)\left(\frac{7}{45}\right)^{n}u[n]$$
$$x_2[n]=4\left(\frac{7}{45}\right)^{n}u[n]$$

Using your properties and the fact that the Fourier transform is linear, you should be able to solve it.