documentclass{article}

usepackage{lipsum}

makeatletter
endlinechar=-1

newcountshortvbox@lines

% #1: Number of lines in the final box
% #2: Width of the box
% #3: Text
longdefshortvbox#1#2#3{
    begingroup
    setbox0=vtop{hsize=#2 #3par}
    setbox2=vtop{unvcopy0shortvbox@{#1}C}
    setbox2=vtop{unvcopy0shortvbox@{#1}B}
    vtop{hsize=#2unvbox1parnoindentstrutldotspar}
    endgroup
}

% #1: number of lines to reassemble
% #2: C = count lines only, otherwise also build box
defshortvbox@#1#2{
    begingroup
    globalsetbox1=vtop{}
    if#2C
        globalshortvbox@lines=0relax
    fi
    loop
        count1=lastnodetype
        ifnumcount1=1relax  % hbox
            setbox10=lastbox
            globaladvanceshortvbox@lines by if#2C 1else -1fi
        fi
        ifnumcount1=11relax  % glue
            skip10=lastskip
            unskip
        fi
        ifnumcount1=13relax  % penalty
            count10=lastpenalty
            unpenalty
        fi
%    message{lastnodetype=thecount1}
    edef@stop{
        ifnumcount1<0 0else
        ifnumcount1=1 1else
        ifnumcount1=11 1else
        ifnumcount1=13 1else
        0% stop early if we don't know how to handle the last node
        fifififi
    }
    if@stop0
    else
        if#2Celse
        globalsetbox1=vtop{
            ifnumshortvbox@lines<#1relax
                ifnumcount1=1relax  % hbox
                    box10
                fi
                ifnumcount1=11relax  % glue
                    vskipskip10
                fi
                ifnumcount1=13relax  % penalty
                    penaltycount10
                fi
                unvbox1
            fi
        }
        fi
    repeat
    endgroup
}

endlinechar=`^^M
makeatother

begin{document}

fbox{shortvbox{7}{5cm}{What if I have got a (possibly long) text that I would like to typeset in a 5cm wide minipage, textbf{ragged right}, so that it uses at most 6 lines?
vskip2ex
Basically, I would just like to ask LaTeX to typeset a piece of text so that we add line breaks as usual at most 5 times, and then the last line is truncated (with some kind of a truncation marker such as texttt{"..."}) if needed.}}
hskip1em
fbox{shortvbox{4}{5cm}{raggedright What if I have got a (possibly long) text that I would like to typeset in a 5cm wide minipage, textbf{ragged right}, so that it uses at most 6 lines?
vskip2ex
Basically, I would just like to ask LaTeX to typeset a piece of text so that we add line breaks as usual at most 5 times, and then the last line is truncated (with some kind of a truncation marker such as texttt{"..."}) if needed.}}

shortvbox{4}{linewidth}{lipsum}

end{document}