diff --git a/compiler/src/dotty/tools/dotc/transform/GenericSignatures.scala b/compiler/src/dotty/tools/dotc/transform/GenericSignatures.scala
index 76408f3f14ac..bdd339482ab3 100644
--- a/compiler/src/dotty/tools/dotc/transform/GenericSignatures.scala
+++ b/compiler/src/dotty/tools/dotc/transform/GenericSignatures.scala
@@ -283,7 +283,7 @@ object GenericSignatures {
           jsig(atp, toplevel, primitiveOK)
 
         case hktl: HKTypeLambda =>
-          jsig(hktl.finalResultType)
+          jsig(hktl.finalResultType, toplevel, primitiveOK)
 
         case _ =>
           val etp = erasure(tp)
diff --git a/tests/pos/i5720.scala b/tests/pos/i5720.scala
new file mode 100644
index 000000000000..3906b288c1ec
--- /dev/null
+++ b/tests/pos/i5720.scala
@@ -0,0 +1,95 @@
+// Ensure we omit valid JVM generic signatures when upper bounds are primitive
+// types. Java generic signatures cannot use primitive types in that position.
+
+class AUnit[B[_] <: Unit]
+class ABoolean[B[_] <: Boolean]
+
+class AByte[B[_] <: Byte]
+class AChar[B[_] <: Char]
+
+class AShort[B[_] <: Short]
+class AInt[B[_] <: Int]
+class ALong[B[_] <: Long]
+
+class AFloat[B[_] <: Float]
+class ADouble[B[_] <: Double]
+
+class ValClU(val i: Unit) extends AnyVal
+class AValClU[B[_] <: ValClU]
+class ValClI(val i: Int) extends AnyVal
+class AValClI[B[_] <: ValClI]
+
+package object opaquetypes {
+  opaque type Logarithm = Double
+  object Logarithm {
+    class ALogarithm[B[_] <: Logarithm]
+    type ALog = ALogarithm[[x] => Logarithm]
+    type ALogD = ALogarithm[[x] => Double]
+    type ALogN = ALogarithm[[x] => Nothing]
+
+    type A1Log = opaquetypes.ALogarithm[[x] => Logarithm]
+    // type A1LogD = opaquetypes.ALogarithm[[x] => Double]
+    type A1LogN = opaquetypes.ALogarithm[[x] => Nothing]
+
+    class ALogNested[B[_] <: Logarithm]
+    class ValClLogNested(val i: Logarithm) extends AnyVal
+    class AValClLogNested[B[_] <: ValClLogNested]
+
+    type A = AValClLogNested[[x] => ValClLogNested]
+    type AN = AValClLogNested[[x] => Nothing]
+  }
+  class ValClLog(val i: Logarithm) extends AnyVal
+  class AValClLog[B[_] <: ValClLog]
+  type AClLog = AValClLog[[x] => ValClLog]
+  type AClLogN = AValClLog[[x] => Nothing]
+
+  class ADouble[B[_] <: Double]
+  type AD = ADouble[[x] => Double]
+  type ADN = ADouble[[x] => Nothing]
+
+  class ALogarithm[B[_] <: Logarithm]
+  type ALog = ALogarithm[[x] => Logarithm]
+  type ALogN = ALogarithm[[x] => Nothing]
+
+  type A1Log = Logarithm.ALogarithm[[x] => Logarithm]
+  type A1LogN = Logarithm.ALogarithm[[x] => Nothing]
+}
+
+object Main {
+  type AU = AUnit[[x] => Unit]
+  type AUN = AUnit[[x] => Nothing]
+
+  type AB = ABoolean[[x] => Boolean]
+  type ABN = ABoolean[[x] => Nothing]
+
+
+  type ABy = AByte[[x] => Byte]
+  type AByN = AByte[[x] => Nothing]
+
+  type AC = AChar[[x] => Char]
+  type ACN = AChar[[x] => Nothing]
+
+
+  type AS = AShort[[x] => Short]
+  type ASN = AShort[[x] => Nothing]
+
+  type AI = AInt[[x] => Int]
+  type AIN = AInt[[x] => Nothing]
+
+  type AL = ALong[[x] => Long]
+  type ALN = ALong[[x] => Nothing]
+
+
+  type AF = AFloat[[x] => Float]
+  type AFN = AFloat[[x] => Nothing]
+
+  type AD = ADouble[[x] => Double]
+  type ADN = ADouble[[x] => Nothing]
+
+
+  type ACU = AValClU[[x] => ValClU]
+  type ACUN = AValClU[[x] => Nothing]
+
+  type ACI = AValClI[[x] => ValClI]
+  type ACIN = AValClI[[x] => Nothing]
+}