In rectangle \(ABCD\), \(AB=5\) and \(BC=3\). Points \(F\) and \(G\) are on \(\overline{CD}\) so that \(DF=1\) and \(GC=2\). Lines \(AF\) and \(BG\) intersect at \(E\). The area of \(\triangle AEB\) is in the form \(\frac{k}{m}\). Please find the value of \(k + m\).

Let's think step by step and output the final answer within \boxed{}.
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