5e doesn't have in its core rules a "charge" action similar to 3.5e's where you can both dash and attack on the same round, if your movement is in a straight line to a target.
By a charge action I mean any action that allows a melee attacker to move more than his usual move distance toward the target and also make a melee attack. The way I imagine a charge action, there may be some benefit to the attack from the attacker's momentum, and some penalty for the single-mindedness of purpose.
There is now the Charger feat which allows:
When you use your action to Dash, you can use a bonus action to make one melee weapon attack or to shove a creature.
If you move at least 10 feet in a straight line immediately before taking this bonus action, you either gain a +5 bonus to the attack's damage roll (if you choose to make a melee attack and hit) or push the target up to 10 feet away from you (if you choose to shove and you succeed).
Is there a house-rule variant that would allow a charge action without the feat, but that imposes a logical negative consequence for doing it without the feat? If house-ruling in charging without the feat weakens the feat too much, a corresponding house rule to strengthen the feat would also be welcome.
I would like especially to hear from people who have actual experience house-ruling this.