Let's see.
NORMAL MAGIC ITEM STUFF
cloak of resistance +1
1,000gp
always-on resist energy, only half the normal resistance?
Well, resist energy is a 2nd-level spell, so lvl 2 x CL 3 x 2,000gp = 12,000gp But... we're looking at half the resistance, (5 instead of 10), so this should be maybe 6,000gp
Stacking two abilities usually is 1.5x the cost of the lesser-priced abilities, so this so far would be worth 7,500gp.
INTELLIGENT MAGIC ITEM STUFF
The mental stats you're using aren't really very intelligent, and according t the chart there's no charge for those. The rule say they're supposed to start at 10, so this really should be Int 10, Wis 10, Cha 10 (still no cost), but I imagine you have some reason you want a dumb and unpleasant intelligent cloak. Also, no Ego score yet.
Telepathy costs 1,000gp and +1 Ego (though I don't know what an Int 6 cloak has to say in people's heads)
Sense 60ft costs 500gp.
Darkvision costs 500gp.
Casting a 1st-level spell 3/day costs 1,200gp and +1 Ego.
The base item costs 7,500gp (cloak plus resistance), so that's a further +2 to Ego.
SUMMARY
That all totals up to 10,700gp with an Ego score of 4.
The +1 resistance is pretty straightforward. A +1 resistance bonus to saves has a base market price of 1,000 gp.
The fire resistance 5 is a bit trickier. A minor ring of energy resistance grants resistance 10 to one energy type and has a market price of 12,000 gp; the energy resistance armor quality grants resistance 10 to one energy type and has a market price of 18,000 gp; a blazing robe grants fire resistance 5, as well as a +1 CL to spells with the fire descriptor and a 1/day burst of fire (20 ft radius, 2d6, Ref DC 16 for half), with a market price of 11,000 gp. The market price increases for major and greater rings of energy resistance (28,000 gp for resistance 20 and 44,000 gp for resistance 30) and improved and greater energy resistance armor qualities (42,000 gp for resistance 20 and 66,000 gp for resistance 30) indicate that pricing progression (with the armor qualities at x1.5 price of the rings) formula is ((resistance / 2.5) - 1) x 4,000 gp; I would put the fire resistance 5 at a base market price of 4,000 gp.
A cloak that provides both a +1 resistance bonus to saves and fire resistance 5 would have a market price of (1,000 gp x 1.5) + 4,000 gp = 5,500 gp.
Per the Intelligent Items rules: "An intelligent magic item has a base price increase of 500 gp." Market price 5,500 gp + 500 gp = 6,000 gp.
"Intelligent magic items possess all three mental ability scores: Intelligence, Wisdom, and Charisma. Each one of these ability scores begins at a value of 10, but can be increased to as high as 20."
Baseline 10 Int, 10 Wis, 10 Cha; assuming the item will be casting burning hands based on Wis (shaman list)*, increasing Wis to 12 adds +500 gp and +1 Ego. Market price 6,000 gp + 500 gp = 6,500 gp.
Telepathy adds +1,000 gp and +1 Ego, Senses 60ft adds +500 gp, and Darkvision adds +500 gp. Market price 6,500 gp + 1,000 gp + 500 gp + 500 gp = 8,500 gp.
Casting a 1st-level spell 3/day adds +1,200 gp and +1 Ego. A burning hands with CL 5* and Wis 12* will do 5d4 damage in a 15 ft cone (Ref DC 12 for half). Market price 8,500 gp + 1,200 gp = 9,700 gp.
Ego will be (item base price, not counting intelligent item enhancements, of 5,500 gp [between 5,000 and 10,000 gp) +2 (12 Wis) +1 (Telepathy) +1 (burning hands 3/day) +1 = 5.
*- except for a staff, a magic item does not cast spells using the owner's ability scores or CL
I think 6,000gp is high--cost usually goes at the square of the bonus. Thus I would be more inclined towards 3,000gp here.Let's see.
always-on resist energy, only half the normal resistance?
Well, resist energy is a 2nd-level spell, so lvl 2 x CL 3 x 2,000gp = 12,000gp But... we're looking at half the resistance, (5 instead of 10), so this should be maybe 6,000gp
Except it isn't. As DragonChess Player has pointed out the ring of energy resistance is the precedent item we're looking for. Resistance 10 costs 12,000gp. 20 costs 28,000gp and 30 costs 44,000gp.
resist energy as a use-activated or continuous effect is spell-level x caster level x 2,000gp.
For resist 10, it's 2 x 3 x 2,000gp = 12,000gp. Matches the ring.
For resist 20, it's 2 x 7 x 2,000gp = 28,000gp. Matches the ring.
For resist 30, it's 2 x 11 x 2,000gp = 44, 000gp. Matches the ring.
Arguably, 4 caster levels adds resistance 10, so if we were trying for resist 15, we'd probably aim for CL 5th. So walking that backwards, for resist 5 we'd be looking for CL 1st. Which can't actually cast the spell. But if undercasting were a thing for this, it'd be 2 x 1 x 2,000gp = 4,000gp.
Which does match DragonChess Player's value. I did miss the base 500gp that gets added to everything else.
I also wasn't thinking about the item needing to have a valid ability score to cast a spell.
It's also worth pointing out that this is all expecting this thing to be CL 1st. So that's what the burning hands would be as well. Reflex DC13 for 1d4.