If you say that a die roll of 5 or lower fails and 15 or better always works, then for half the rolls proficiency is not counted. Take the example of an athletics check Bobby the Barbarian has a +8 to his athletics, he should never fail a DC 5 check even on a 1. Presto the Wizard has a -1 to his athletics so if the DC is 15 they would fail an athletics check by 1 when they roll a 15 if you are following the rules. Meanwhile for some truly difficult tasks of say a 20 or or higher, some people simply shouldn't be able to accomplish it. When the characters are higher levels, sometimes you can have DCs of 25 or higher so you need to be highly skilled and a bit lucky to succeed.
It's a significant difference to whether or not proficiency matters. It's fine if it works for you I would just disagree that it's a good house rule.
I thought you were talking about that part, but wanted to make certain.
The bonuses (i.e. proficiency+) are assumed. We don't use this if you aren't proficient or have a +5 ability. The way it came into being was through attacking. At 1st level, most PCs are +5, so if they roll 15, they hit AC 20. Very few games are going to have AC over 21, so it is a
very safe bet that if you roll 15, you're gonna hit. At the other end, since the minimum AC is often 10 (often higher), a roll below 5 means you missed. So, it is also a safe bet that rolling 5 or lower fails.
Since most skill checks run in the 10-20 range as well, it works for those, too. In your example, Bobby at +8
cannot fail a DC 5 check so the DM would never even call for a roll--it would be pointless and a waste of time.
And to be clear, it is a "general rule of thumb" sort of houserule. Sure, sometimes it might mean someone makes a roll when technically they should have failed by 1, or fails a roll technically they should have made, but frankly it speeds up the game A LOT for our group--its purpose for being--so is actually a really good house rule.