Break it down to simpler forms. You know e^ln(x) = x so try to make something of that form.

5e^3(ln(6))= 5e^(ln(6^3)). Move the in front of the ln to be the power of the 6.

Then we know that e^ln(x) = x, so

5e^(ln(6^3)) = 5 (6^3) = 5(27)(64) = 320(27) = (300+20)(27) = 8100+ 540 = 8640.