TeXForm handling of derivative higher than two

Somewhat hacky:

TeXForm[y'''''[t] + 2 x'''[t] - y'[t] == x[t] /. 
        Derivative[k_Integer][f_] /; k > 2 :> 
        Superscript[f, Symbol[StringJoin[ConstantArray["′", k]]]]]

(* 2 x'''(t)+y'''''(t)-y'(t)=x(t) *)

An alternative to transforming an expression before applying TeXForm is to modify the TraditionalForm formatting rules for Derivative:

Derivative /: MakeBoxes[Derivative[n_Integer?Positive][h_],TraditionalForm] := SuperscriptBox[
    MakeBoxes[h,TraditionalForm],
    StringJoin@ConstantArray["\[Prime]",n]
]

Then, TeXForm will use this new FormatValue:

TeXForm[y'''''[t] + 2 x'''[t] - y'[t] == x[t]]

2 x'''(t)+y'''''(t)-y'(t)=x(t)

and ToString[.., TeXForm] as well:

ToString[y'''''[t] + 2 x'''[t] - y'[t] == x[t], TeXForm]

2 x'''(t)+y'''''(t)-y'(t)=x(t)