2.State, in a stepwise fashion how 250 mL of a 0.100 M Sodium Hydroxide solution

can be made from Sodium Hydroxide pellets.
3. Calculate the needed volume of solution 2 above, that would make a dilute 5 L
solution of 0.05 M Sodium Hydroxide

First you can't make an exact 0.1 M NaOH solution using NaOH pellets because the pellets will pick up CO2 and moisture from the air and convert the NaOH pellets to Na2CO3. This is a slow reaction so you get the Na2CO3 coating on the pellets while weighing them. You can make an APPROXIMATE 0.1 M solution so the directions follow.

How many moles do you need? That's M x L = 0.100 x 0.250 = 0.0250
How many grams is that? That's g = moles x molar mass = 0.0250 x 40 g/mol = 1.00
Therefore, weigh out 1 g NaOH pellets, place in a 250 mL volumetric flask, add some distilled water, swirl to dissolve the pellets, let cool (the flask will get quite hot when the pellets dissolve), add water to the mark on the flask, stopper, mix thoroughly, label. done.
Then to make the dilution, use the dilution formula of mL1 x v1 = mL2 x v2
mL1 is the unknown, v1 = 0.100 solution, m2 is 0.05 M from the problem and v2 is 5,000 mL so
mL1 x 0.100 = 0.05 x 5000
Solve for mL1, take that volume, place it in a 5,000 mL volumetric flask, add enough distilled water to make to the mark on the flask, stopper, mix thoroughly, label. done.