The two systems are quite incompatible. Even the expected range of modifiers is different. 4E characters' skills are even going to be wrong. Further, a lot of 4E character abilities apply modifiers to other characters, something that is very rare in 5E.
Even the spellcasting principles are differently handled.
Saves don't work quite the same; they're directly on attributes, and don't go up with level... unless proficient in them.
Further still, the relative starting survivability is a bit lower in 5E.
These differences mean that, aside from not having matching labels, many of the differences result in the closest comparable ability being significantly different in expected rating.
Also, the weapons list is shorter in 5E, and not entirely the same.
Most core PHB1 4E classes have equivalents. Most but not all.
The attributes are the same, and if using array, even the same before-race-modifiers values. This makes rewriting the character much quicker.
The exception is the warlord. There's no good direct equivalent to it. If you want the same "buff my allies" mechanical role, converting to a cleric or bard is good. If you want the same theme, it's the 5E Battlemaster-Fighter.
All the PHB1 races are in 5E, too... tho Eladrin are buried in the DMG.
So, to convert, figure out the starting array used, apply the racial mods from 5E, take the same number of levels in the same class (and, if eligible, the subclass), select skills, and you're rolling.
It's probably easiest to simply rebuild the character from the concept stage, as important attribute associations are different.
Any of the automated methods (Fifth Edition Character for Android is what I use) can make generating a new character as fast as 5 minutes, including writing it down on paper...