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Black is okay as long as he doesn't respond 5...Nxe4 to 5.d4.

Does Black win more than lose against the Cochrane Gambit?

5. d4 {"Vitolinsh Attack." #1 pop/3. w 50%.}
5. Nc3 {"Lang Attack." #2 pop/3. b 48%.}
5. Bc4+ {"Kirali Attack." #3 pop/3. b 55%.}

The database I'm using shows only three lines of attack for White.  The two least popular lines show Black with the better winning average. Only in the #1 most popular line does White have the better winning average. (The variation names are my own, for reference purposes.)

Per the database, Black's most popular response to the "Lang Attack" is 5...Be7, not 5...c5. At any rate, the database shows only seven games at most as a base for the statistics for each of Black's responses at the 5th move, so those are too few data points for a good assessment.

5...Be7 {#1 pop. b 57%.}
5...Be6 {#2&3 pop. w 60%.}
5...c5 {#2&3 pop. n 60%.}
5...g6 {#4&5 pop. w 100%.}
5...Qe8 {#4&5 pop. wb 50%.}
5...c6 {#6 pop. w 67%.}
5...Bg4 {eolib. w 100%.}

From what I gather from this opening: (1) Black must castle by hand, by moving his king to g7 after moving his rook to f8 (sometimes e8). That's why Black is so eager to play ...Be7 as soon as possible: to make room for his KR to escape the corner. (2) Black is giving back White's gambited material by ...c5 so as not to come under too strong an attack. (3) Remember that this is a gambit, so it can be quite tactical, unlike most Petrov's Defense games.