In the absence of further information from the OP, I have made a few observations and assumptions.
The TQP3M9008 is specified for operation from 50 to 4000MHz. The input and output impedances are specified as 50 Ohm.
Looking at the oscilloscope traces, the wanted signal is a burst of 5MHz when measured in a 50 Ohm system.
Looking at the datasheet for the TQP3M9008, the coupling capacitors are specified as 1000pF for use at 50MHz.
A quick "back of fag packet" calculation shows that the reactance of the coupling capacitors will be 33Ohm at 5 MHz. A source of a few dB loss.
The reactance of the load inductor is about 10 Ohm at 5 MHz. Not high enough for a 50 Ohm system.
So, if the amplifier is set up as per the datasheet, the will be very little gain at 5MHz and plenty of gain at higher frequencies.
+2 on the soldering.
Clean off all that "gunk" (flux ?)
The connector at the input does not appear to be soldered to the groundplane.
The metal case is probably contributing very little (nothing ?) to screening from external noise in the current setup.
Suggestions:
Increase the value of the coupling capacitors and the load inductor by a factor of at least 10.
Add a low pass filter (10MHz cutoff ?) at the output, and maybe the input as well.
Clean up all the gunky flux on the PCB.
JimB