The Basic types of Attacks?

If you have cold and fire, why not add other elemental types such as wind and water?

And the pedant in me cannot resist pointing out that a ballistic attack is simply one type of energy attack, using kinetic energy. Fire and audio are also 'energetic' forms. I expect by energy you mean some kind of radiation attack, such as laser, which is based on electro-magnetic waves.

To further divide the energy catagory, you get:

Kinetic energy: ballistics, physical hitting etc. Audio also comes in this catagory I think.

Radiation: transfer of heat energy via various forms of radiation (visible light, microwave etc)

Nuclear: Energy stored in atomic nucleii is released by splitting or fusing atomic nuclii.

Potential/Gravitational: Energy confered by differences in position.

Perhaps you could do something with these?

Have 5 kinds, in both melee and ranged. 5 x 2 = 10

Like Lordpog said, make 2 groups of 5 types. One for magic and the other one for physical attacks. If you want to make rock-paper-scisor style oppositions, you place your 5 type in a circle and draw a pentragram in it, each line is an opposition.

I'm seeing some confusion in your types. You seem to have some items that are suited to a broad category to attack, and some items that are suited to a manifestation of a broad category.

For instanace, you have Physical (but you really mean physical melee, I suspect) and Ranged. These are clearly broad categories.

Then there is mental, I assume you mean like mind control, or using brain power to harm, or trick a target. This is clearly a ranged attack, but it may be distinct enough to merit its own category.

Next is Psycological. If I interpert you correctly, this is an information attack directed at morale or perhaps even operational knowledge. This is distinct enough to merit a category, too.

After that, electric, heat, cold are all a manifestation of either a melee or ranged attack. As all can be justified as either melee, ranged, or ballistic.

Radiation is clearly a ranged attacks (not ballistic, but could prolly go through opposing obstacles)

Sonic and nasal can be information attacks (misleading scents or sounds, also silencing of sound) or a physical damaging range attack (caustic gas, or deafening sound)

So really, I think you've alread got way more than ten types of attacks.

Melee
Physical (clubs, swords, fists)
Hot (on touch)
Cold (on touch)
Electric (Shock on touch)

Ranged - (direct fire)
Physical (bullets, arrows)
Hot (flamethrower)
Cold (frost ray?)
Electric (lightening bolts - horizontal)
Mental (mind powers)

Ranged - (indirect fire)
Physical (artillery, ICBM, grenades)
Hot (fireball that arcs over stuff)
Electric (summon a storm cloud to send lightening down)
Mental (long-range mind powers)
Sonic (deafening (painful) sond waves)
Nasal (inhalants prolly a better term)

Information
Psycological (propaganda)
Sonic (decoy sounds)
Nasal (decoy scents)

It might be better to focus on the manifestations as your ten proper types, (physical, chemical) and then associate them with various modes of employment (range, melee)

So, with that in mind, here are some types:
1) Physical (fists, bullets)
2) Explosive (HEAT rounds, bombs)
3) Chemical (gas, acid)
4) Biological (viruses, bacteria)
5) Radiation (neutron bombs, light?, lasers?)
6) Mental (mind powers)
7) Tempature (lasers?, electrical?, burning, freezing)
8) Sonic (sound blasts)
9) Water (drownding, short-circuiting)
10) Energy (light?, lasers?, electrical)
11) Time (slowing, haste, ageing)

Some attack modes could be:
1) Melee (requires touching)
2) Direct LOS ranged (guns, lasers)
3) Direct non-LOS rangerd (radiation)
4) Indirect ranged (artillery)
5) Passive (landmines, decoys, traps) Seperate category because while they affect the target from close, they usually are triggered when the attacker is at range. So they are kind of both ranged and not

Then the others might be better in some kind of modifer category:
1) Psycological (misinformation, propaganda)
2) Camoflage (sound, smell, sight, radar)
3) Legal (lawyers, bureacracy, public opnion)

Some attacks could actually be categorized as multiple types:

Flash-bang grenade:
Physical (concussion from shock wave)
Sonic (the bang)
Energy (the flash)
Modes: Indirect Ranged

Low-power laser gun:
Energy
Modes: LOS Ranged

High-power laser gun:
Energy
Radiation
Temperature
Modes: LOS Ranged, non-LOS Ranged for X-Ray laser or something)

Orbital Mind Control Ray:
Mental
Modes: Indirect Ranged (if from a character perspective of play), Direct non-LOS Ranged (if from the satelite perspective of play)

Tsunami Generator:
Water
Physical (from impact of giant wave)

If a target had protection from one of the types in a multiple type attack, it may take recuced damage or effect from the attack.