Short answer: Yes, you can, but it's not really any easier than starting from the ground up and building a new character.
Long answer: While fourth editon D&D shares many setting conceits with 3.5 and earlier editions, the two are very different games in terms of how characters are constructed and the way challenges are addressed during play.
You might want to check out this question about the differences between the two games for a general overview. The accepted answer is pretty good.
So, about converting your character to 3.5... Well, it depends on exactly what you've built, but since 3.5rd and 4th edition make reasonably similar assumptions about setting, it shouldn't be too hard to convert your character's concept across.
However, as you may have noticed, there are a lot of differences between 4th edition and 3.5, most notably including different scales of leveling and a differing level of combat-centric-ness that will likely make it impossible to convert your character without making compromises.
As far as I know, there's no formal downgrade migration path available, so you'll have to do the conversion the old-fashioned way: Hit the 3.5 books and try to work out how your character would fit the system.
Unfortunately, I can't give you more specific advice than that without knowing more about your character. Could you possibly post your character sheet?
It is generally helpful for players to have a Player's Handbook readily available, especially for spellcasters who need to reference spell descriptions every now and then. Aside from that, the most help that it will do is speed up character generation and leveling-up, which is good at the table because it allows for more game-time in the session. I find that in a party of 4 players and 1 DM, having two Player's Handbooks available is generally acceptable for our group, though more would be spectacular. In your case, your table should have 3-4, possibly one of which would be for the DM to reference behind the screen.
Hope that helped give you some additional perspective on the matter!
Best Answer
No, they're very different games. Anything you try to use out of the D&D 5e Player's Handbook will be nonsense to the “game engine” that a D&D 3.5e game uses. It would be like trying to put a Blu-ray disc into a CD-ROM drive: it will superficially look like it fits, but it will not function.
To play in their 3.5e game, ask them what you need. They may lend you a 3.5e PHB, or they may just point you to the d20 System Reference Document and give you some guidance on how to build a character (which is missing from the d20 SRD on purpose), or they may have a different set of information to use for making characters in their particular campaign. Ask and find out.