what kind of waveform are you amplifying? if it's a sine wave, the op amp needs a bandwidth of 5 Mhz or more. if it's not a sine wave, it should be an op amp with 50Mhz or more bandwidth. the bandwidth is shown as the Gain Bandwidth Product, which means the frequency at which the op amp's gain is 1 without feedback. you are looking for a gain of 5, so the amp needs to be capable of a gain of 5 at 1Mhz. if it's not a sine wave,the amp needs to be capable of amplifying harmonics of the fundamental frequency, which requires a much greater bandwidth. in the chart below, you see where the gain curve crosses 0db (i.e. a gain of 1) at 10Mhz. this particular op amp has a GBW of 10Mhz, and at 1Mhz is capable of a gain of 10 (which is 20db on the chart). this op amp (TLE2072) would work ok at a gain of 5 for a sine wave, but only a sine wave, because with a square or triangle wave, the harmonics (which change the shape of the wave) will not be amplified the same as the fundamental frequency sine wave. within the audio and ultrasonic ranges it will work fine, but as you approach 1Mhz, the lack of amplification for harmonics will make it look more and more like a sine wave.
if you find this kind of confusing, understand that a pure sine wave only consists of it's fundamental frequency. if you have a square wave or triangle wave, it's harmonics of the fundamental frequency that get added to the sine wave that change it's shape. if you pass a square wave through an amplifier that only amplifies the fundamental frequency, the harmonics go away and you have a sine wave again.