Working through the skill material, I notice almost immediately the reduction of the number of skills. Also the skill proficiency simplifies keeping track of known skills with the same bonus applied to all proficient skills. A character is either proficient or not.
On the side, I have been working with the Modern D20 system.
Here is what I have seen so far for my skill conversion:
Climb, Jump, & Swim -> Athletics
Balance & Tumble -> Acrobatics
Hide & Move Silently -> Stealth
Sleight of Hand stays the same
Search, Research, & Listen -> Investigation
Navigate -> Nature
Knowledge -> History & Religion
Handling Animal -> Animal Handling
Sense Motive -> Insight
Treat Injury -> Medicine
Spot -> Perception
Survival stays the same
Bluff & Disguise -> Deception
Intimidate -> Intimidation
Perform -> Performance
Diplomacy -> Persuasion
This will convert the core of the game's skill system. There are however skills that don't translate which may have to be added to the 5e system.
I appreciate the reduction in the number of skills - the main ones being Athletics, Acrobatics, Stealth, Investigation, and Deception - which combine 12 skills into these 5 skills.