Question about current output of a DC-DC stepdown converter
The output power of the DC-DC converter is equal to the input power multiplied by converter efficiency. I assumed your DC-DC converter has an efficiency off 80%.

\$P_{out} = P_{in} \cdot 80\% \$

\$ 3I_{out} = 5I_{in} \cdot 0.8 \$

\$I_{out} = 1.33I_{in}\$

But not always. You get the maximum current that is supported by the converter. If that limit is reached, then this equation is not true anymore.