Nimbostratus
Cirrocumulus
On your switch (Assuming it's a cisco), setup a trunked interface (Either physical or etherchannel. I recommend a channel and use active LACP). In cisco world a channel is what a PC person would call teaming or link aggregation. Trunking in cisco world is 802.1Q VLAN tagging.
On your F5 setup a trunk (Which is LACP based link aggregation). Then create tagged VLAN's on that trunk. You can have quite a few (In fact Im not even sure what the actual limit is. Both devices will do extended VLAN ID's. On the cisco you'll have to enable it. On the F5 it will do extended ID's by default.
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