Having a hard time finding this information. Is the POE out on the RB5009UPr+S+IN POE or POE+? Does POE out require the use of the 2-pin terminal?
Neither. 
Each port can provide 440 mA:
https://mikrotik.com/product/rb5009upr_s_in
0.44A48V=21.12 W (typical voltage)
0.44A57V=25.08 W (max voltage)
802.3af 15.40 W @PSE /12.95 W @PD (POE)
802.3at 30.00 W @PSE / 25.50 W @PD (POE+)
The triple power input should be irrelevant, but only ether1 Is 802.3af/at and of course you cannot push to It more than 25-30W (because otherwise the POE Power supply wouldn’t be compliant.
So, either jack or pins if you want 48-57 V and some 3 A total power to match the 150 W max declared on specs.
Well speaking about the datasheet, it definitely states:
PoE out: 802.3af/at
Which is PoE/PoE+
As for this
It’s only stated for PoE-In so I would expect the “PoE-out ports: Ether1-Ether8” means all ports “can do” 802.3af and at.
Sure, but if you Power a 16 W device with 30 W (max of the 802.3at Power supply) you can expect to draw, total of the other 7 ports, 14 W or so.
If you prefer a 802.3at Power supply can Power - chained - no more than 2 x 802.3af like devices, let’s say the RB5009 and an AP connected to one of the PoE out ports.
So, if you plan to PoE power multiple devices from several ports with PoE out, the RB5009 needs a beefy power supply that has to be connected to either the jack or DC pins.
As an example the 48V2A96W, should be enough to power the RB5009 and 7 x cAP Ax’s, 711 W+116 W= 93 W considering that real life used power Is usually a little less than what is in specs and that kind of power is not reachable even with 802.3bt type 4.
thanks. I’m trying to power 2 Netgear WAX620 access points. The product data sheet says the device uses 25.5W. Seems like the 5009 will underpower them using the supplied barrel connector power supply?
That is a beast of access point.
And it is a strange beast, as the datasheet:
https://www.downloads.netgear.com/files/GDC/WAX620/WAX620_DS.pdf
says that it can even be powered by 802.3af (though losing some 40% of performance) 
.
No idea if it is a sort of “switch” 60%/100% or if it is linear, i.e. at 48V 21.12/25.50=82.82%
I don’t think that it is “exact math” (i.e. in real life one of those AP’s will need less than the declared 25.50 W) but surely you would have to raise the voltage to the max (57V) to have some 25.00 W that - probably, even considering some loss due to cable - would be enough in practice, but surely you are right on the border and you would need a 57V power supply with (16+2*25)*1.10=73 Watt at least.
That ( 57V power supply with 1.5 or 2A) will likely cost something in the 70-90 US$ range that you have to consider.
All in all, personally I would think of a “normal” RB5009 (saving some 299US$-219=80 US$)
https://mikrotik.com/product/rb5009ug_s_in
and either a separate PoE power supply and injector capable of powering two 802.3at devices or two simple 802.3at power supplies.
Only as an example, two of these:
https://www.planet.com.tw/en/product/poe-165?c1=power-over-ethernet&c2=poe-injector-splitter&c3=802-3at-poe-plus-injector
should be obtainable for around 45 dollars each, so the budget remains roughly the same.
Or a Poe+ Switch? I think that 5 or 8 ports one with 90W power budget or so can be found in the 100-120 US$ range, as an example the Netgear GS305EPP:
https://www.downloads.netgear.com/files/GDC/GS305EP/GS305EP_GS305EPP_GS308EP_GS308EPP_GS316EP_GS316EPP_DS.pdf