Yes: At 5th level, extra attack includes the Longbow
The Fighter, Barbarian, Monk, Ranger and Paladin all get Extra Attacks at fifth level. None of them specify "melee" or "ranged" therefore there is no limitation per the rules as written. All of them read the same way.
Beginning at 5th level, you can attack twice, instead of once, whenever you take the Attack action on your turn.
Weapons Properties for the Longbow show no restriction
There is no stated restriction on longbow attacks. If the longbow had a special property beyond Heavy, Two-Handed, or Ammunition it would be listed in the Weapons Properties section of the PHB and on the table.
I recommend that you discuss this with the DM before the next game session - before play begins. Based on the game's mechanics/rules, the longbow does not have the same loading feature as the Hand Crossbow and the Heavy Crossbow. At 5th level, each turn you can attack twice with the Longbow. (My Ranger enjoys doing this now that he's fifth level). If the DM rules otherwise after this discussion, then you'll need to figure out if you can live with that or not.
Excerpted from the Weapons table on page 48 Basic Rules (Same info in PHB):
\begin{array}{r|ccc}
\text{} & \text{Martial Ranged Weapons} \\
\hline
\text{Crossbow, hand} & \text{1d6 piercing} & \text{light} & \text{__} & \mathbf{\text{loading}} \\
\text{Crossbow, heavy} & \text{1d10 piercing} & \text{heavy} & \text{two-handed} & \mathbf{\text{loading}} \\
\text{Longbow} & \text{1d8 piercing} & \text{heavy} & \text{two-handed} & \text{__} \\
\end{array}
Loading. Because of the time required to load this weapon, you can fire only one piece of ammunition from it when you use an action, bonus action, or reaction to fire it, regardless of the number of attacks you can normally make. (Basic Rules p. 48; also in the Weapons Properties section of the PHB)
There is no Loading property for Longbow, unlike the two crossbows on that list; thus there is no "once per action" limitation with that weapon.