[Closed] AKs NL5, is this spot a fold instead?

Is it right to push this flop with as much money invested preflop? I put villian on a overpair on this board, is this how to extract as much value as possible? I am actually a favor against a range of TT+ AQs AKo AKs

56% favor against his entire range in this pot.

Hand converted with online PokerStrategy.com hand converter:

Play hand

$0.02/$0.05 No-Limit Hold'em (9 handed)

Known players:
[tg]MP1$5.11:///////;MP2$5.78:///////;MP3$3.09:///////;CO$7.84:///////;BU$9.61:///////;SB (Hero)$5.00:///////;BB$5.31:///////;UTG1$6.90:///////;UTG2$1.89:///////;[/tg]

Preflop: Hero is SB with K:c, A:c.
2 folds, MP1 raises to $0.17, MP2 folds, MP3 raises to $0.58, 2 folds, Hero raises to $1.96, 2 folds, MP3 calls $1.38.

Flop: ($4.14) 8:c, T:d, 5:c (2 players)
Hero bets $3.04, MP3 calls $1.13(All-In).

Turn: ($8.31) Q:h (2 players)

River: ($8.31) 4:s (2 players)

Final Pot: $8.31.

Results follow:

Hero shows high card ace(Kc Ac).
MP3 shows a pair of jacks(Jh Jc).

MP3 wins with a pair of jacks(Jh Jc).