It depends upon the level disparity and several other factors... most especially which methods of experience gain you use.
5E & Level Disparity
5E is FAR more forgiving of mixed level parties than most other editions of D&D.
It's fair to state that mixed level parties in 3E or 4E were major problems, in that they broke the careful balance of the encounter design mechanics.
In AD&D (1E and 2E), and in Cyclopedia/BECMI/BX D&D, mixed level parties were all but inevitable - but there were no carefully worked out balance systems, and due to the way experience was generally awarded by the rules as written, parties tended to have wizards of about 2/3 the level of fighters, and thieves higher still.
5E was built to allow for dissimilar levels; ideally, characters from the same tier will be good fits for other characters within that tier. The total modifiers will be similar, and the range of the abilities by class will also be comparable.
To recap the tiers:
I. Levels 1-4
II. Levels 5-10
III. Levels 11-16
IV. Levels 17-20
(V). Epic (level 20 with one or more epic boons)
"Standard XP Rules"
If you use the standard rules, which, to recap, include:
- XP shared for defeated monsters
- XP shared for traps survived &/or defeated
- Individual XP for Roleplay &/or session (= easy encounter)
- Individual XP for Chapter or Major Accomplishment (= moderate encounter)
Using those benchmarks, it's quite possible for a PC to come to a reasonably useful level in a reasonable number of sessions. They're always going to lag, but will be within a level or two fairly quick, as fair challenges for a high level party are sometimes instant level gains for low level characters.
Catching Up in Standard XP
The character will naturally catch up with, but not equal, the party. Unless, of course, they get more major goal or roleplay bonuses than the other members.
It's reasonable to allow a bonus for being behind, but the rules don't support it.
Using Chapter Leveling
If using the "Chapter leveling", the character will not catch up until Epic Tier. Which isn't a good thing. If the difference is 2-3 levels, it's noticeable, but not really problematic after about level 4.
The solution in this case is to offer anyone below average party level an extra chance to level up mid-chapter.
The Gygaxian Old School Way
Everyone sets aside the high level characters for a couple months to let the new guy experience the lower level play.
It's inherently fair, but it interrupts storylines, and many times, players won't go back to the originals. It did, however, need to be mentioned.
The game isn't going to break if one character is 2-3 levels behind. It does change the encounter math a bit, but it's not a huge issue.
That said, whether one should or not boils down to a group nature. Competitive personality types might actually be offended by giving a new player "free XP", while some group players will whinge about an inequality.
Also, the learning curve on character classes is steep for some - having those lower levels down really helps the higher level play.
Bottom Line: Ask your Players.
It's your Choice to make, but you should ask the rest of the group for input, not strangers on the internet. We don't have to live with the consequences, you and your players do.