A list of weights are given as 78 kg, 96 kg, 84 kg, 66 kg, and 94 kg. If 14 kg is added to each weight, and then another 5 kg is added to each weight, what are the new weights?

The total amount to be added to each initial weight is $14 \text{ kg} + 5 \text{ kg}$.

$$14 \text{ kg} + 5 \text{ kg} = 19 \text{ kg}$$

So, for each initial weight, we will add $19 \text{ kg}$.

1. Initial weight: $78 \text{ kg}$

   $$78 \text{ kg} + 19 \text{ kg} = 97 \text{ kg}$$

   This matches the given first value.

2. Initial weight: $96 \text{ kg}$

   $$96 \text{ kg} + 19 \text{ kg} = 115 \text{ kg}$$

3. Initial weight: $84 \text{ kg}$

   $$84 \text{ kg} + 19 \text{ kg} = 103 \text{ kg}$$

4. Initial weight: $66 \text{ kg}$

   $$66 \text{ kg} + 19 \text{ kg} = 85 \text{ kg}$$

5. Initial weight: $94 \text{ kg}$

   $$94 \text{ kg} + 19 \text{ kg} = 113 \text{ kg}$$

The completed list of final weights is:

1. $97 \text{ kg}$
2. $115 \text{ kg}$
3. $103 \text{ kg}$
4. $85 \text{ kg}$
5. $113 \text{ kg}$

The final answers are:

1. $\boxed{\text{97 kg}}$
2. $\boxed{\text{115 kg}}$
3. $\boxed{\text{103 kg}}$
4. $\boxed{\text{85 kg}}$
5. $\boxed{\text{113 kg}}$