I connect a 5 volts to a low resistance, but I measure a much lower current than I expect
The user manual of your multimeter tells us why:

In the current measuring mode (DC or AC): input impedance approximately 3&nbsp;k&Omega;.

Which in all honesty is just a joke.

So with 5 V the most current you can get is 1.67&nbsp;mA, but it doesn't even tell us the range of the input impedance, so the value you measured is "fine".

It says to be able to measure up to 4&nbsp;mA (which is another joke), you need at least 12&nbsp;V to get close to the measuring range by creating a "short" with your test leads.

Actually we can calculate the input impedance for your meter to be: 5.12&nbsp;V / 1.367&nbsp;mA - 15&nbsp;&Omega; = 3730&nbsp;&Omega;.

A good meter has something in the range of 10&nbsp;&Omega; or less, depending on the selected range. The µCurrent, for example, has 0.02&nbsp;&Omega; for mA measurement, 10&nbsp;&Omega; for µA measurement and 10&nbsp;k&Omega; for nA measurement.