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JavaScript (ES6), 132 bytes

f=N=>(F=n=>N?n<30?F[k=n%5]^(F[k]|=1<<(v=Math.random()*15))?(n++-17?"_BINGO"[n]||k*15-~v:'free')+` 
`[k>>2]+F(n):F(n):`
`+f(N-1):n)``

Try it online!

Commented

f = N => ( // outer function taking the number N of grids
 F = n => // inner function taking a counter n
 N ? // if there's still a grid to process:
 n < 30 ? // if n is less than 30:
 F[k = n % 5] // k is the column index in [0..4]
 ^ // if F[k] is not equal to its updated value
 ( F[k] |= 1 << ( // where the floor(v)-th bit is set
 v = // where v is
 Math.random() // randomly picked in [0,15[
 * 15 //
 )) ? // then:
 ( n++ - 17 ? // if this is not the center cell:
 "_BINGO"[n] // append either a BINGO letter (if n <= 5)
 || // or
 k * 15 - ~v // the number k * 15 + floor(v + 1)
 : // else:
 'free' // append the word 'free'
 ) + //
 ` \n`[k >> 2] + // append a line-feed if k = 4,
 // or a space otherwise
 F(n) // append the result of a recursive call to F
 : // else:
 F(n) // try again
 : // else:
 `\n` + // append a line-feed followed by
 f(N - 1) // the result of a recursive call to f
 : // else:
 n // stop the recursion
)`` // initial call to F with n zero'ish