While an argument can be made either way, my general experience is that 5e is actually less random than previous versions and when it isn't, it is generally due to the choices of the GM. Previous editions did have much higher modifiers, but the DCs for challenges is also much different than in previous editions. For example the table of DCs for 5e puts "very easy" tasks at 5 and "nearly impossible" is set at 30. In the same table for 3.5e "very easy" is at 0 and "nearly impossible" is at 40. So why are these DCs so different?
Earlier editions effectively tried to overcome the randomness of the dice using high modifiers, thus making the roll contribute less to the overall score. The problem with this is even when you have a very high bonus, the dice still makes up more than 50% of the range of scores you can get. With a reasonably high +10 bonus you are equally likely to barely squeak past in a task of "average" difficulty as you are to complete a "Heroic" feat. With that same +10 it also means that someone with a +0 in that same skill will do as well or better than you 13.75% of the time, which is pretty frequently considering this is basically someone trying something for the first time and beating a trained professional.
5e took a completely different approach by changing how and when you roll the dice. Rather than just taking straight dice rolls 5e uses the system of advantage and disadvantage to actually change the distribution of the dice, making high numbers much more likely in favorable conditions and much less likely in unfavorable ones. This means that you are unlikely to have a party member who has never been to your home town know their way around better than you as you would have advantage and they would have disadvantage. This generally makes the game a lot more flexible so that if you should succeed on a skill check, you generally will rather than the newbie beating the pro scenario we described earlier.
The second place 5e changed things is in when you roll dice with the introduction of passive skill checks. This basically acts like Pathfinder's concept of taking a 10 (though under slightly different conditions) where you can skip rolling for routine or repeated tasks and just add 10 to your modifier. Since you don't roll, you know exactly what your check will be and it avoids the all too common scenario of having the eagle eyed ranger who you sent to scout rolling a 1 and leading everyone into a trap.
One of the major themes of the changes in 5e is giving more power back to the GM than the last few editions. This does mean that the "feel" of the game will depend a lot on how your GM decides to run it. If they choose to be selective with applying advantage and disadvantage or ignore passive checks, then the game will feel much more random. If on they go to the other extreme, applying advantage to one side and disadvantage to the other in every scenario and using passive checks liberally, the game will feel almost predetermined with nearly no randomness at all. In general though, I think it is relatively easy to make the system feel "right" where things you "should" succeed at are very likely to certain, things you "shouldn't" are very unlikely to impossible, but most other things fall in the middle keeping the excitement of "will this work?".