I am suggesting that in this SB-28 case, camera P mode will not be a good or best choice. The SB-28 is an old flash that has no CLS communication with the camera hot shoe. Its non-TTL A mode automation can still work well, but the camera really does not know the flash is even present. The camera automation is not working for the flash. This just means you have to watch out a little closer, and work around it.
I would use camera M mode for SB-28 flash indoors. Set maybe f/5 for bounce flash (ISO 400 under 8 or 10 foot ceiling) and set maybe 1/60 to 1/200 second shutter speed. Camera A mode normally works here, but with old SB-28 flash, you surely get an extremely slow shutter speed indoors. Camera M mode lets you set it too, to control what is happening randomly.
It is a bigger story, but P mode chooses whatever aperture choice it thinks the ambient light needs. It may choose any one aperture choice of many. But in this non-TTL auto mode, you also have to manually program that aperture setting into the flash menu. But then P mode can change that aperture somewhat before you get to click off your picture. Auto ISO can also change it. So you may have camera automation busy changing things that the fixed flash cannot respond to.
I think you will seriously want to use camera M mode with indoor flash (any time the ambient light level is low and negligible), so you can set a fixed aperture that will stay fixed, and which you can choose to be suitable for the flash power too. Also of course, Auto ISO definitely should be turned Off (you also have to program ISO into the flash menu).
The f/5 is the same f/5 (same to the flash) if f/5 is set in camera A, M, or P mode, but it will stay f/5 in A or M mode (it will be whatever you set it to be).
Slightly more advanced skill, but the advantage of M mode (indoors) is that you can then also set any shutter speed, to better control the ambient. The automatic flash is still automatic in camera M mode... it adjusts its power level to the aperture specified (and ISO and distance, etc). The ambient is dim indoors, it does not much matter. The indoor ambient is dimmer than say 1/60 second would provide for, so the ambient indoors is always underexposed, which is the reason we are using flash. And the flash does not care about shutter speed, so basically, shutter speed is a don't care value indoors (not quite always true, dim ambient can have some effect, but camera M mode allows use to set the shutter speed we want to control it).
There are lots of things going on in the P mode automation. The old SB-28 flash does not know about any of it. P mode does not choose any of it for the undetected flash. You will need to control it yourself.
In the D300, ISO will stay at Minimum ISO if the flash is detected present (but the SB-28 is not detected present, so turn Auto ISO off with flash).
Newer models work different, they set Auto ISO for the ambient, not for the flash (so turn Auto ISO off with flash).
P mode enforces a maximum aperture with flash, which varies slightly with camera model, but probably f/4 or f/5 for an external flash (probably f/2.8 for the internal flash), or the maximum the lens can actually do. This means you do have a little better chance of it staying fixed (at say f/4), but the SB-28 is not detected present. And if no flash is detected, in dim light indoors where flash is needed, the lens is probably always wide open in P mode (with no flash detected). You probably want to stop down a stop or so however, for sharper results.
Also the camera automation enforces a minimum shutter speed if flash is detected present. D300 and D700 have the E1 menu for this, but default is 1/60 second MINIMUM shutter speed for flash, for camera A or P mode (because we are using flash, and we don't need a very slow shutter). But the SB-28 is not detected, so shutter speed is whatever the dim ambient meters, like maybe 1/4 second. But you don't want to use 1/4 second for flash. You are using flash, which the non-present Minimum shutter speed was to protect you from. So... using camera M mode simply lets you set any shutter speed you do want to use, maybe 1/60 second (allows a bit of the orange ambient in), or maybe 1/200 second which keeps the orange ambient out)...
Outdoors, for fill flash in the bright sun (to fill the dark harsh shadows), P mode is a natural then, because it also meters correctly for the very bright ambient. P mode knows it cannot use a shutter speed faster than camera maximum sync speed (1/200 second on many, 1/250 second on yours). But the SB-28 is not reported present, so P mode and A mode surely tries to use a fast shutter speed, 1/1000 second or faster, which of course cannot work with flash. You cannot allow shutter speed to exceed maximum sync speed (normally automation controls this, but no communication on the older SB-28).
Summary: I am suggesting the easy way for the SB-28 (which is not known present to todays camera) is:
First thing: Turn Auto ISO off (this flash cannot react to changes)
Indoor flash: Camera M mode. Bounce flash, ISO 400, f5, maybe 1/100 second. This generally ought to about always work - because the flash is automatic).
Outdoor fill flash in sun, Camera A mode (for the ambient), which will have to be up around f/11 to prevent shutter speed from exceeding maximum sync speed, like say 1/200 second (or 1/250 on your two). Or you could determine a correct M mode exposure with acceptable shutter speed (sometimes desired to slightly underexpose the ambient).
Camera P or S mode will allow aperture to change on the unsuspecting flash.
Don't forget though, for fill flash in sun - we have to adjust fill flash to be around -2 EV lower (to be fill instead of main light). Otherwise the sum of ambient and flash will overexpose subject by one stop. This reduction is automatically done in modern TTL BL mode, and it is manually done for modern TTL flash (using flash compensation about -2 EV).
For the SB-28, you can lie to the flash, and set its menu to an ISO 4x higher than is actually used, to get this -2 EV compensation.
But camera P mode is not going to protect the undetectable flash either indoors or outdoors.
