If there was only one possible way for 5 numbers to be separated byno more than 26 and you'd said 4 coins all landing heads up, you'd bealmost right. 26 is fairly close to half of the possible numbers, sofor each number drawn there's about a 50% chance that it will be in thelower half. That's roughly the same as each coin being flipped having a50% chance of landing heads.
In reality there are many ways for the 5 numbers to be separated by26 or less. They can all fall in the bottom or top range, from 1 to 26or 34 to 59, but they could also fall in any of 32 other ranges,between 2 to 27 and 33 to 58. That's 34 different ranges of 26,compared to only one way for 4 coins to all land heads. Comparing it to4 coins is the right way, because no matter what the first number is itallows the rest to fall within a range of 26. The actual probabilityis very complex, since it varies with the first number drawn. If thefirst number is between 26 and 34 then 50 of the remaining 58 numbersfall within a range of 26, so it's very likely that the next numberwill fall in that range. The least likely way for all of the numbers tobe within a range of 26 would be if the first number was 1 or 59,because then there are only 25 numbers that fall in the range. Let'ssee how likely that would be.
The chances that the 2nd number will be between 2 and 26 (or 34 and58) is 25/58, or .43. Assuming that happens, there's a 24/57 chancethat the 3rd number will fit, or .42. For the 4th number it's 23/56, or.41. For the 5th number it's 22/55, or .4. Putting it all together wehave .43*.42*.41*.4 =.296, or a hair under 3%. That's 1 in 33.7. So nomatter what the first number is there's at least a 1 in 33.7 chancethat the next 4 will fall within a range of 26.
For any first number other than 1 or 59, there's a greater chance that the 2nd number will fit the range. Asnoted above, there are 9 numbers, that if drawn first result in a 50/58or .86 chance that the 2nd number will fall in the range. The chancesthat the 3rd number will fall in the range will depend on the 2ndnumbers relation to the first. Again, let's take the worst case, wherethe 2nd number is at the end of the range. The chances of the 35d, 4thand 5th numbers falling in the range would be the same, so the overallchance becomes .96*.42*.41*.4 or .066. That's 6.6% or 1 in 15, almostidentical to the 1 in16 chance that flipping 4 coins will result in 4heads.
Overall, the range is most likely to be greater than 26, but a range of 26 or less is hardly a very unusual event.
I've ignored the 6th number, because without specifying which of the 6 it makes no difference.