From D&D 3.5 to 5.0(5E) - 4 - Movement in Combat in 5th Edition Rules

In 5.0 your characters and your enemies will enjoy a little more freedom of movement.  The rules allow you to break up your move distance during your turn.  Thus you can move, attack, then move again.  A fighter with the Extra Attack feature and a speed of 25 could move 10 feet, make an attack, move another 10 feet and make another attack, and then move 5 more feet.  A Wild Elf with a speed of 35 could move 20 feet, cast a spell, then move another 15 feet.

Sticking with movements in 5 foot increments is recommended, especially if you are playing with minis on a grid.  But if your game is entirely verbal then you may feel free to tell the DM you are moving in 1 foot increments.  In either case, some affects are measured in 1 foot increments.  For example, if your character is crawling, for every 1 foot costs you an extra foot of movement.  Moving through difficult terrain also costs you one foot of movement for every foot you move.  Thus that Wild Elf with a speed of 35 could move 17 feet through difficult terrain, or perhaps 10 feet through difficult terrain followed by an attack, and then 15 feet of movement through normal terrain.