You can try the newspaper but use a lot more than 5 sheets. You can also try cardboard from appliance boxes.
I really hate fabric in a bed. You can not cultivate. You will eventually have to remove it which is an unbelievable pain.
Your best bet is to remove the weeds. Add soil if needed. If you are not adverse to chemicals work in a pre-emergent - Amaze or Preen. Read and follow the label directions. Good for about 6 months of weed control.
Once the beds are cleaned add a thick layer of mulch. If you use wood mulch use 4". Wood mulch is good for water retention but really does not do much for weed control. A thick layer of pine straw is great for both water retention and weed control. Get bales of pine straw and put down a VERY thick layer - 8" to 12". It will be a little unsightly in the beginning but will quickly pack. Once it has packed it is very attractive and few weed seeds will be able to germinate. Pine straw decomposes slower than wood mulch so you do not have to replenish as often. NO the pine straw will not have an adverse affect on your soil. The decomposing pine straw does not significantly lower the pH of the soil.
Elizabeth - or Your Majesty
Living and growing in Lafayette, La.
When weeding, the best way to make sure you are removing a weed and not a valuable plant is to pull on it. If it comes out of the ground easily, it is a valuable plant. ~Author Unknown