If you are going by the fantasy size of the tire then you may well have the wrong tube. You need to look for the ISO or ETRTO size on the tire. Sometimes it's easy to find, other times it's part of the tiniest print embossed on the sidewall. The proper format is nn X nnn where nn is the tire casing width (roughly) and the nnn is the BSD, bead seat diameter of the tire. Same convention is used for rims but it's the internal width of the rim at the bead seat and the BSD. If your tire is a 27 five, then your tire might have something like 65 x 584 on it somewhere. Don't confuse if with the fantasy size which is usually written in big letters on the tire.
Sometimes the tire makers use a bastardized ETRTO convention and will have something like 700 x 25C. You just have to know that a 700c tire is 622 BSD and that the "c" after 25 usually means crochet or hooked rims or tire bead.
Now on to tubes....
You want a tube that just fits the inside of your tire and rim. Too much excess and you might have folds and kinks that you can feel while riding and will cause wear on the tube every revolution of the tire. Too little width on the tube and you'll be blowing it up to fill the voids between it and the tire/rim and that will mean you've stretched the tube thinner making it more prone to puncture and acting like a balloon and suddenly going flat instead of gradually flatting from a puncture.
Many tubes will have a range of size tires they fit. Make sure your tire is within that range. Different makers show that range differently, but many will have something that helps you. You are mostly interested in width because you typically don't want to use tubes intended for one BSD tire in another. It can be done, but not desired except for impossible to find anymore sizes or emergencies when you have to have something.
You mentioned you couldn't fit a schrader in your rim. I would have thought most 584 BSD rims would be schrader as they are typically wider rims and the bigger valve stem diameter isn't an issue for them. But maybe not. I don't speak mountain bike very well. <grin> You sure what you have is a real 27.5 or 27 five tire?