Good battery simulators will be expensive because they will need two power regulators, one working to produce output and one to absorb input. I recommend the Keithley.
If you are really struggling with cost you could use a straightforward 10 A power supply and put a resistive 5A load on it. This should do what you want, at a loss of efficiency!
Robert Franke-Lang : A (somewhat) cheaper supply is the Keithley 2303, I think just a single channel version of the 2306. Really low cost solutions can be built using power (operational) amplifiers (e.g. https://www.ti.com/lit/an/slva618/slva618.pdf). You may need to modify the circuit and use a higher output current opamp to achieve 5A.