First hand at the table, Good shove or bad?

My very first hand at the table so my blind was put in for me and I was able to check. No reads since I just sat down.

PokerStars No-Limit Hold'em, $0.02 BB (7 handed) - Poker-Stars Converter Tool from FlopTurnRiver.com

SB ($2.79)
Villain (BB) ($4.42)
UTG ($0.47)
MP1 ($3.53)
MP2 ($0.82)
Hero (CO) ($2)
Button ($0.60)

Preflop: Hero is CO with 3, 6
UTG calls $0.02, MP1 calls $0.02, MP2 calls $0.02, Hero (poster) checks, 2 folds, Villain checks

Flop: ($0.11) J, 5, 5 (5 players)
Villain checks, UTG checks, MP1 checks, MP2 checks, Hero checks

Turn: ($0.11) 4 (5 players)
Villain checks, UTG checks, MP1 checks, MP2 checks, Hero checks

River: ($0.11) 7 (5 players)
Villain bets $0.48, 3 folds, Hero raises to $1.98 (All-In), Villain calls $1.50

Total pot: $4.07 | Rake: $0.20

Should I have pushed?

My thinking:
My thought was (after his river bet) that he had a set of 5's and slowplayed the crap out of them and was just tossing a bet out there or he had an equal straight.

He could have the 5, but if he checks all the way to the river and bids, maybe the river card helped him. He could have 68 or 77. I mean you need to put him on a range. Most people play very straight forward I think.

going AI in a limped pot is for the nuts
his overbet screams omg I just got the nuts

just call imo because you're beating only trips, but you're behind bigger straights and he's most likely to have:
1. 86
2. 77
3. 75

it's very hard for him to play the hand this way if the river card didn't improve his hand

just call imo because you're beating only trips, but you're behind bigger straights and he's most likely to have:
1. 86
2. 77
3. 75

it's very hard for him to play the hand this way if the river card didn't improve his hand

I agree. The problem I had with this hand is that I hadn't had a stellar session. In a 2 hour span I had a straight lose to a higher straight, a set lose to a flush and a flush to a higher flush....
after a while you just think "man I can't be behind again..."
Of course as we all know....you can!