Supposing your load is \$5\:\textrm{A}\$ and you are interested in learning about BJTs, you have two options for the final power stage BJT -- NPN or PNP. Sometimes, this is determined by things like "common cathode" or "common anode" arrangements in your load, so you are forced to choose one or the other. Sometimes, you get to pick how your load is tied so you can choose either.
For something in this current compliance range, you should be thinking about a TO-220 style package (or better.) A power BJT will drop some \$V_{CE}\$ across the switch, no matter what you do about it, and all of that times the current becomes power that has to be dissipated; plus whatever the base requires, as well. And at these currents, everything adds up.
A best case scenario is that you find a good quality power BJT that has decent gain at a collector current of \$5\:\textrm{A}\$, is multi-sourced, and is cheap and readily available. The D44H and D45H series qualifies. They are widely sourced, widely available, and cheap. About 40 cents from Arrow right now, in ones (as an example) for the PNP D45H11.
This PNP provides a guaranteed minimum \$h_{FE}=40\$ with \$I_C=4\:\textrm{A}\$. The actual gain of any given device is likely better. But I think you can plan on that figure here. The guaranteed worst case voltage drop limiting the load's voltage compliance is stated at \$I_C=8\:\textrm{A}\$ as \$V_{CE\left(sat\right)}=1\:\textrm{V}\$. But the typical value at your current is about 4 times better than that, or \$V_{CE\left(sat\right)}=250\:\textrm{mV}\$. The guaranteed worst case base-emitter drop at \$I_C=8\:\textrm{A}\$ is \$V_{BE\left(sat\right)}=1.5\:\textrm{V}\$, but the typical value is \$V_{BE\left(sat\right)}=1\:\textrm{V}\$.
A circuit for this might look like:
simulate this circuit – Schematic created using CircuitLab
I first estimated the base current for \$Q_1\$ as \$I_{B_1}=\frac{5\:\textrm{A}}{\beta_1=40}=125\:\textrm{mA}\$. I set up a small current in \$R_1\$ to help pull the base up when \$Q_2\$ goes OFF. (About 2% of the base current.) \$V_{BE\left(sat\right)_1}=700 - 1500\:\textrm{mV}\$, so the base voltage may be \$3.5 - 4.3\:\textrm{V}\$. \$Q_3\$ is operated as a switch and I assumed \$V_{CE\left(sat\right)_2}=200-400\:\textrm{mV}\$ (and \$\beta_2=20\$.) This leaves \$R_3\$ having to drop \$3.2-4.1\:\textrm{V}\$ while also providing a minimum of \$125\:\textrm{mA}+2.5\:\textrm{mA}\approx 128\:\textrm{mA}\$. In the worst case, this would suggest \$R_3=25\:\Omega\$, but I decided to use \$R_3=27\:\Omega\$ as a nearby standard value. Given that I don't actually expect the absolute worst case of \$V_{BE\left(sat\right)_1}=1.5\:\textrm{V}\$, I think this is reasonable.
I computed the required base current for \$Q_2\$ as \$6.4\:\textrm{mA}\$. With a worst case \$V_{BE\left(sat\right)_2}=1\:\textrm{V}\$, that would imply \$R_2=625\:\Omega\$. But the standard value of \$R_2=560\:\Omega\$ guarantees a little more base current, which won't hurt any here.
Worst case power dissipations of interest are shown, as well. As you can see, \$R_3\$ will have to be a \$1\:\textrm{W}\$ resistor. The D45H11 probably won't actually dissipate \$5.1\:\textrm{W}\$, which is only in a highly unusual worst case situation. (Much more likely it will be closer to \$1-2\:\textrm{W}\$.)
Just be aware that the load may not get access to more than \$4.3-4.5\:\textrm{V}\$ and that it could see as little as \$4.0\:\textrm{V}\$ in the unusual worst case scenario.
A similar design process can be used to achieve this with the D44H11 NPN power BJT, as well.
These details are part of the reason that a MOSFET might be recommended in situations like this. They are more expensive and perhaps less widely sourced, but \$R_3\$ also isn't cheap and it takes up space. So you have to make decisions in your own situation about what works for you.
For me as a hobbyist? I have bucket loads of nearly free BJTs -- less than a half cent apiece for small signal and typically less than 10 cents each for TO-220. (I shop around.) So I usually use those, as well as giving them out to others by the hand-full. Stocking up on MOSFETs sets back my budget way too much for that freedom. So I use discrete MOSFETs somewhat sparingly.