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More info please. A 5'X5' section is kind of large for a simple repair, unless you mean it has some gouges or rough areas and can be sanded and refinished.
If you are talking about an area that has cracked or rotted than you will have to remove the section and replace.
Is this an older home with the original hardwood over a crawl space or a new home with the flooring over concrete slab?
My tool of choice here would be a Fein Multimaster. There are knockoffs available cheaper than their c.$300++ price tag. These tools will make plunge cuts and have a scraper blade to remove old adhesive.
The tricky part is finding same size material for replacement and finishing to match. Generally you will be doing a whole room re-finish.
It is time consuming, but you can do it. Carefully remove the baseboard and then starting in the center of the damaged area, next to the wall, take a flat bar and hammer and remove the center board. From there you can work each way out until the damaged wood is removed.
You will have to take a stiff, large blade putty knife and remove any glue from the concrete
You are now ready to re-install the new boards. The last board, you will probably have to remove the tung by carefully cutting with a hand saw or depending on the style of flooring, you might be able to use a stright blade. If the ends of the new boards have a tung and groove, remove the tung only if neccessary. When you cut the new pieces, cut them about 3/8" shorter then your measurement. You can then slide the piece in place by using the flat bar wedged against the wall with a little block of wood and prying it into place.
Your base board should cover this gap.
Make sure the glue does not come through the last board where you cut the tung off.
Re-install the base board and a little caulk and touch up paint and your done.
The Fein multimaster is a great tool with many other uses that costs in excess of three bills, but there are knockoffs suiable for a one time job such as the Harbor Freight for less than fifty bucks