The eval() function evaluates an expression, but "5+5" is a string, not an expression. Use parse() with text=<string> to change the string into an expression:
> eval(parse(text="5+5"))
[1] 10
> class("5+5")
[1] "character"
> class(parse(text="5+5"))
[1] "expression"
Calling eval() invokes many behaviors, some are not immediately obvious:
> class(eval(parse(text="5+5")))
[1] "numeric"
> class(eval(parse(text="gray")))
[1] "function"
> class(eval(parse(text="blue")))
Error in eval(expr, envir, enclos) : object 'blue' not found